Verfügbarkeit: Mathematical analysis | Technische Universität München

Mathematical analysis: linear and metric structures and continuity

Gespeichert in:

Bibliographische Detailangaben
Beteiligte Personen:	Giaquinta, Mariano 1947- (VerfasserIn), Modica, Giuseppe 1948- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Boston [u.a.] Birkhäuser 2007
Schlagwörter:	Algèbre linéaire Analyse fonctionnelle Análise funcional Continu (Mathématiques) Espaces vectoriels Fonctions (Mathématiques) Lineaire algebra Matrizes (álgebra) (teoria) Ruimten (wiskunde) Topologie Álgebra linear Algebras, Linear Continuum (Mathematics) Functional analysis Functions Vector spaces Analysis
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016540091&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XVIII, 465 S. Ill., graph. Darst.
ISBN:	9780817643744 0817643745

Internformat

MARC


LEADER	00000nam a2200000 c 4500
001	BV023356538
003	DE-604
005	20080820
007	t\|
008	080623s2007 xx ad\|\| \|\|\|\| 00\|\|\| eng d
020			\|a 9780817643744 \|9 978-0-8176-4374-4
020			\|a 0817643745 \|9 0-8176-4374-5
035			\|a (OCoLC)123954872
035			\|a (DE-599)BVBBV023356538
040			\|a DE-604 \|b ger \|e rakwb
041	0		\|a eng
049			\|a DE-355
050		0	\|a QA184.2
082	0		\|a 515 \|2 22
084			\|a SK 130 \|0 (DE-625)143216: \|2 rvk
100	1		\|a Giaquinta, Mariano \|d 1947- \|e Verfasser \|0 (DE-588)111595738 \|4 aut
245	1	0	\|a Mathematical analysis \|b linear and metric structures and continuity \|c Mariano Giaquinta ; Giuseppe Modica
264		1	\|a Boston [u.a.] \|b Birkhäuser \|c 2007
300			\|a XVIII, 465 S. \|b Ill., graph. Darst.
336			\|b txt \|2 rdacontent
337			\|b n \|2 rdamedia
338			\|b nc \|2 rdacarrier
650		4	\|a Algèbre linéaire
650		4	\|a Analyse fonctionnelle
650		7	\|a Análise funcional \|2 larpcal
650		4	\|a Continu (Mathématiques)
650		4	\|a Espaces vectoriels
650		4	\|a Fonctions (Mathématiques)
650		7	\|a Lineaire algebra \|2 gtt
650		7	\|a Matrizes (álgebra) (teoria) \|2 larpcal
650		7	\|a Ruimten (wiskunde) \|2 gtt
650		7	\|a Topologie \|2 gtt
650		7	\|a Álgebra linear \|2 larpcal
650		4	\|a Algebras, Linear
650		4	\|a Continuum (Mathematics)
650		4	\|a Functional analysis
650		4	\|a Functions
650		4	\|a Vector spaces
650	0	7	\|a Analysis \|0 (DE-588)4001865-9 \|2 gnd \|9 rswk-swf
689	0	0	\|a Analysis \|0 (DE-588)4001865-9 \|D s
689	0		\|5 DE-604
700	1		\|a Modica, Giuseppe \|d 1948- \|e Verfasser \|0 (DE-588)133455777 \|4 aut
856	4	2	\|m Digitalisierung UB Regensburg \|q application/pdf \|u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016540091&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA \|3 Inhaltsverzeichnis
943	1		\|a oai:aleph.bib-bvb.de:BVB01-016540091

Datensatz im Suchindex

_version_	1819319857530798080
adam_text	Contents Preface Part I. Linear Algebra 1. Vectors, Matrices and Linear Systems .................. 3 1.1 The Linear Spaces Kn and Cn .......................... 3 a. Linear combinations .......................... 3 b. Basis ....................................... 6 с Dimension ................................... 7 d. Ordered basis ................................ 9 1.2 Matrices and Linear Operators ......................... 10 a. The algebra of matrices ....................... 11 b. A few special matrices ........................ 12 с Matrices and linear operators .................. 13 d. Image and kernel ............................. 15 e. Grassmann s formula ......................... 18 f. Parametric and implicit equations of a subspace .. 18 1.3 Matrices and Linear Systems ........................... 22 a. Linear systems and the language of linear algebra 22 b. The Gauss elimination method ................. 24 с The Gauss elimination procedure for nonhomogeneous linear systems ................ 29 1.4 Determinants ........................................ 31 1.5 Exercises ............................................ 37 2. Vector Spaces and Linear Maps ......................... 41 2.1 Vector Spaces and Linear Maps ........................ 41 a. Definition ................................... 41 b. Subspaces, linear combinations and bases ........ 42 с Linear maps ................................. 44 d. Coordinates in a finite-dimensional vector space .. 45 e. Matrices associated to a linear map ............. 47 f. The space C(X,Y) ........................... 49 g. Linear abstract equations ...................... 50 ¡с Contents h. Changing coordinates ......................... 51 і. The associated matrix under changes of basis .... 53 j. The dual space C(X, K) ....................... 54 k. The bidual space ............................. 55 1. Adjoint or dual maps ......................... 56 2.2 Eigenvectors and Similar Matrices ...................... 57 2.2.1 Eigenvectors .................................... 58 a. Eigenvectors and eigenvalues ................... 58 b. Similar matrices .............................. 60 с The characteristic polynomial .................. 60 d. Algebraic and geometric multiplicity ............ 62 e. Diagonizable matrices ......................... 62 f. Triangularizable matrices ...................... 64 2.2.2 Complex matrices ............................... 65 a. The Cayley-Hamilton theorem ................. 66 b. Factorization and invariant subspaces ........... 67 с Generalized eigenvectors and the spectral theorem 68 d. Jordan s canonical form ....................... 70 e. Elementary divisors ........................... 75 2.3 Exercises ............................................ 76 3. Euclidean and Hermitian Spaces ........................ 79 3.1 The Geometry of Euclidean and Hermitian Spaces ........ 79 a. Euclidean spaces ............................. 79 b. Hermitian spaces ............................. 82 с Orthonormal basis and the Gram-Schmidt algorithm .................................... 85 d. Isometries ................................... 87 e. The projection theorem ....................... 88 f. Orthogonal subspaces ......................... 90 g. Riesz s theorem .............................. 91 h. The adjoint operator .......................... 92 3.2 Metrics on Real Vector Spaces ......................... 95 a. Bilinear forms and linear operators ............. 95 b. Symmetric bilinear forms or metrics ............ 97 с Sylvester s theorem ........................... 97 d. Existence of g-orthogonal bases ................ 99 e. Congruent matrices ...........................101 f. Classification of real metrics ...................103 g. Quadratic forms ..............................104 h. Reducing to a sum of squares ..................105 3.3 Exercises ............................................2.09 Contents xi 4. Self-Adjoint Operators .................................. Ill 4.1 Elements of Spectral Theory ........................... Ill 4.1.1 Self-adjoint operators ............................ Ill a. Self-adjoint operators ......................... Ill b. The spectral theorem .........................112 с Spectral resolution ............................114 d. Quadratic forms ..............................115 e. Positive operators ............................117 f. The operators A* A and AA* ...................118 g. Powers of a self-adjoint operator ................119 4.1.2 Normal operators ...............................121 a. Simultaneous spectral decompositions ...........121 b. Normal operators on Hermitian spaces ..........121 с Normal operators on Euclidean spaces ..........122 4.1.3 Some representation formulas .....................125 a. The operator A*A ............................125 b. Singular value decomposition ..................126 с The Moore—Penrose inverse ....................127 4.2 Some Applications ....................................128 4.2.1 The method of least squares ......................128 a. The method of least squares ...................128 b. The function of linear regression ................130 4.2.2 Trigonometric polynomials .......................130 a. Spectrum and products .......................131 b. Sampling of trigonometric polynomials ..........132 с The discrete Fourier transform .................134 4.2.3 Systems of difference equations ...................136 a. Systems of linear difference equations ...........136 b. Power of a matrix ............................137 4.2.4 An ODE system: small oscillations ................141 4.3 Exercises ............................................143 Part II. Metrics and Topology 5. Metric Spaces and Continuous Functions ...............149 5.1 Metric Spaces ........................................151 5.1.1 Basic definitions ................................151 a. Metrics .....................................151 b. Convergence .................................153 5.1.2 Examples of metric spaces .......................154 a. Metrics on finite-dimensional vector spaces ......155 b. Metrics on spaces of sequences .................157 c. Metrics on spaces of functions ..................159 5.1.3 Continuity and limits in metric spaces .............161 a. Lipschitz-continuous maps between metric spaces . 161 b. Continuous maps in metric spaces ..............162 cii Contents c. Limits in metric spaces ........................164 d. The junction property .........................165 5.1.4 Functions from R™ into Mm ......................166 a. The vector space С°{А,Ш.т) ................... 166 b. Some nonlinear continuous transformations from W1 into Жы .............................167 c. The calculus of limits for functions of several variables ....................................171 5.2 The Topology of Metric Spaces .........................174 5.2.1 Basic facts .....................................175 a. Open sets ...................................175 b. Closed sets ..................................175 с Continuity ...................................176 d. Continuous real-valued maps ...................177 e. The topology of a metric space .................178 f. Interior, exterior, adherent and boundary points .. 179 g. Points of accumulation ........................180 h. Subsets and relative topology ..................181 5.2.2 A digression on general topology ..................182 a. Topological spaces ............................182 b. Topologizing a set ............................184 с Separation properties .........................184 5.3 Completeness ........................................185 a. Complete metric spaces .......................185 b. Completion of a metric space ..................186 с Equivalent metrics ............................187 d. The nested sequence theorem ..................188 e. Baire s theorem ..............................188 5.4 Exercises ............................................190 6. Compactness and Connectedness .......................197 6.1 Compactness .........................................197 6.1.1 Compact spaces ................................197 a. Sequential compactness .......................197 b. Compact sets in Ж™ ...........................198 с Coverings and e-nets ..........................199 6.1.2 Continuous functions and compactness .............201 a. The Weierstrass theorem ......................201 b. Continuity and compactness ...................202 с Continuity of the inverse function ..............202 6.1.3 Semicontinuity and the Fréchet-Weierstrass theorem 203 6.2 Extending Continuous Functions .......................205 6.2.1 Uniformly continuous functions ...................205 6.2.2 Extending uniformly continuous functions to the closure of their domains ..........................206 6.2.3 Extending continuous functions ...................207 a. Lipschitz-eontinuous functions .................207 Contents xiii 6.2.4 Tietze s theorem ................................208 6.3 Connectedness .......................................210 6.3.1 Connected spaces ...............................210 a. Connected subsets ............................211 b. Connected components ........................211 с Segment-connected sets in Ж™ ..................212 d. Path-connectedness ...........................213 6.3.2 Some applications ...............................214 6.4 Exercises ............................................216 7. Curves ..................................................219 7.1 Curves in Rn ........................................219 7.1.1 Curves and trajectories ..........................219 a. The calculus .................................222 b. Self-intersections .............................223 c. Equivalent parametrizations ...................223 7.1.2 Regular curves and tangent vectors ................224 a. Regular curves ...............................224 b. Tangent vectors ..............................225 с Length of a curve .............................226 d. Arc length and C1-equivalence .................232 7.1.3 Some celebrated curves ..........................233 a. Spirals ......................................234 b. Conchoids ...................................236 с Cissoide..................................... 237 d. Algebraic curves ..............................238 e. The cycloid ..................................238 f. The catenary ................................240 7.2 Curves in Metric Spaces ...............................241 a. Functions of bounded variation and rectifiable curves .............................241 b. Lipschitz and intrinsic reparametrizations .......243 7.2.1 Real functions with bounded variation .............244 a. The Cantor- Vitali function ....................245 7.3 Exercises ............................................247 8. Some Topics from the Topology of Жп ...................249 8.1 Homotopy ...........................................250 8.1.1 Homotopy of maps and sets ......................250 a. Homotopy of maps ...........................250 b. Homotopy classes .............................252 с Homotopy equivalence of sets ..................253 d. Relative homotopy ............................256 8.1.2 Homotopy of loops ..............................257 a. The fundamental group with base point .........257 b. The group structure on ττχ (X, Хо) ...............257 с Changing base point ..........................258 Contents d. Invariance properties of the fundamental group .. . 259 8.1.3 Covering spaces .................................260 a. Covering spaces ..............................260 b. Lifting of curves ..............................261 с Universal coverings and homotopy ..............264 d. A global invertibility result ....................264 8.1.4 A few examples .................................266 a. The fundamental group of S1 ..................266 b. The fundamental group of the figure eight .......267 с The fundamental group of Sn, η > 2............267 8.1.5 Brouwer s degree ................................268 a. The degree of maps S1 -> S1 ...................268 b. An integral formula for the degree ..............269 с Degree and inverse image ......................270 d. The homological definition of degree for maps S1 -> S1 ............................271 8.2 Some Results on the Topology of Жп ....................272 8.2.1 Brouwer s theorem ..............................272 a. Brouwer s degree .............................272 b. Extension of maps into Sn .....................273 с Brouwer s fixed point theorem .................274 d. Fixed points and solvability of equations in M™ 1 1 . 275 e. Fixed points and vector fields ..................276 8.2.2 Borsuk s theorem ...............................278 8.2.3 Separation theorems .............................279 8.3 Exercises ............................................281 Part III. Continuity in Infinite-Dimensional Spaces 9. Spaces of Continuous Functions, Banach Spaces and Abstract Equations .................................285 9.1 Linear Normed Spaces ................................285 9.1.1 Definitions and basic facts .......................285 a. Norms induced by inner and Hermitian products . 287 b. Equivalent norms .............................288 с Series in normed spaces .......................288 d. Finite-dimensional normed linear spaces .........290 9.1.2 A few examples .................................292 a. The space £p, 1 < ρ < oo ......................292 b. A normed space that is not Banach .............293 c. Spaces of bounded functions ...................294 d. The space e^Y) .............................295 9.2 Spaces of Bounded and Continuous Functions ............295 9.2.1 Uniform convergence ............................295 a. Uniform convergence ..........................295 b. Pointwise and uniform convergence .............297 Contents xv c. A convergence diagram ........................297 d. Uniform convergence on compact subsets ........299 9.2.2 A compactness theorein..........................300 a. Equicontinuous fonctions ......................300 b. The Ascoli-Arzelà theorem ....................301 9.3 Approximation Theorems ..............................303 9.3.1 Weierstrass and Bernstein theorems ...............303 a. Weierstrass s approximation theorem ............303 b. Bernstein s polynomials .......................305 с Weierstrass s approximation theorem for periodic functions ....................................307 9.3.2 Convolutions and Dirac approximations ............309 a. Convolution product ..........................309 b. Mollifiers ....................................312 с Approximation of the Dirac mass ...............313 9.3.3 The Stone-Weierstrass theorem ...................316 9.3.4 The Yosida regularization ........................319 a. Baire s approximation theorem .................319 b. Approximation in metric spaces ................320 9.4 Linear Operators .....................................322 9.4.1 Basic facts .....................................322 a. Continuous linear forms and hyperplanes........323 b. The space of linear continuous maps ............324 с Norms on matrices ...........................324 d. Pointwise and uniform convergence for operators . 325 e. The algebra End (Χ) ..........................326 f. The exponential of an operator .................327 9.4.2 Fundamental theorems ...........................327 a. The principle of uniform boundedness ...........328 b. The open mapping theorem ....................329 с The closed graph theorem .....................330 d. The Hahn-Banach theorem ....................331 9.5 Some General Principles for Solving Abstract Equations ... 334 9.5.1 The Banach fixed point theorem ..................335 a. The fixed point theorem .......................335 b. The continuity method ........................337 9.5.2 The Caccioppoli-Schauder fixed point theorem .....339 a. Compact maps ...............................339 b. The Caccioppoli-Schauder theorem .............341 с The Leray-Schauder principle ..................342 9.5.3 The method of super- and sub-solutions ............342 a. Ordered Banach spaces ........................343 b. Fixed points via sub- and super-solutions ........344 9.6 Exercises ............................................344 xvi Contents 10. Hubert Spaces, Dirichlet s Principle and Linear Compact Operators.....................................351 10.1 Hubert Spaces.......................................351 10.1.1 Basic facts .....................................351 a. Definitions and examples ......................351 b. Orthogonality ................................354 10.1.2 Separable Hubert spaces and basis ................355 a. Complete systems and basis ...................355 b. Separable Hubert spaces .......................355 с Fourier series and 1%..........................357 d. Some orthonormal polynomials in L2 ...........360 10.2 The Abstract Dirichlet s Principle and Orthogonality .....363 a. The abstract Dirichlet s principle ...............364 b. Riesz s theorem ..............................366 с The orthogonal projection theorem .............367 d. Projection operators ..........................368 10.3 Bilinear Forms .......................................368 10.3.1 Linear operators and bilinear forms ...............369 a. Linear operators ..............................369 b. Adjoint operator .............................369 с Bilinear forms ................................370 10.3.2 Coercive symmetric bilinear forms .................371 a. Inner products ...............................371 b. Green s operator .............................372 с Ritz s method ................................373 d. Linear regression .............................374 10.3.3 Coercive nonsymmetric bilinear forms .............376 a. The Lax-Milgram theorem ....................376 b. Faedo-Galerkin method .......................377 10.4 Linear Compact Operators ............................378 10.4.1 Fredholm-Riesz-Schauder theory .................378 a. Linear compact operators ......................378 b. The alternative theorem .......................379 с Some facts related to the alternative theorem .... 381 d. The alternative theorem in Banach spaces .......383 e. The spectrum of compact operators .............384 10.4.2 Compact self-adjoint operators ...................385 a. Self-adjoint operators .........................385 b. Spectral theorem .............................387 с Compact normal operators ....................388 d. The Courant-Hiibert-Schmidt theory ...........390 e. Variational characterization of eigenvalues .......392 10.5 Exercises ............................................393 Contents xvii 11. Some Applications......................................395 11.1 Two Minimum Problems..............................395 11.1.1 Minimal geodesies in metric spaces................ 395 a. Semicontinuity of the length ...................395 b. Compactness .................................396 c. Existence of minimal geodesies .................397 11.1.2 A minimum problem in a Hilbert space ............397 a. Weak convergence in Hilbert spaces .............398 b. Existence of minimizers of convex coercive functionals ..................................400 11.2 A Theorem by Gelfand and Kolmogorov .................402 11.3 Ordinary Differential Equations ........................403 11.3.1 The Cauchy problem ............................404 a. Velocities of class Ck{D) ......................404 b. Local existence and uniqueness .................405 c. Continuation of solutions ......................407 d. Systems of higher order equations ..............409 e. Linear systems ...............................410 f. A direct approach to Cauchy problem for linear systems .....................................411 g. Continuous dependence on data ................413 h. The Peano theorem ...........................415 11.3.2 Boundary value problems ........................416 a. The shooting method .........................418 b. A maximum principle .........................419 с The method of super- and sub-solutions .........421 d. A theorem by Bernstein .......................423 11.4 Linear Integral Equations ..............................424 11.4.1 Some motivations ...............................424 a. Integral form of second order equations ..........425 b. Materials with memory ........................425 с Boundary value problems ......................426 d. Equilibrium of an elastic thread ................427 e. Dynamics of an elastic thread ..................427 11.4.2Volterra integral equations .......................429 11.4.3 Fredholm integral equations in C° .................430 11.5 Fourier s Series .......................................431 11.5.1 Definitions and preliminaries .....................433 a. Dirichlet s kernel .............................435 11.5.2 Pointwise convergence ...........................436 a. The Riemann-Lebesgue theorem ...............436 b. Regular functions and Dini test ................437 11.5.3 L2-convergence and the energy equality ............439 a. Fourier s partial sums and orthogonality .........439 b. A first uniform convergence result ..............440 с Energy equality ..............................441 11.5.4 Uniform convergence ............................442 xviii Contents a. A variant of the Riemann-Lebesgue theorem .....442 b. Uniform convergence for Dini-continuous functions ....................................444 c. Riemann s localiziation principles ...............445 11.5.5 A few complementary facts .......................445 a. The primitive of the Dirichlet kernel ............445 b. Gibbs s phenomenon ..........................447 11.5.6 The Dirichlet-Jordan theorem ....................449 a. The Dirichlet-Jordan test .....................449 b. Féjer example ................................451 sums ....................................452 A. Mathematicians and Other Scientists ...................455 B. Bibliographical Notes ...................................457 С Index ...................................................459
any_adam_object	1
author	Giaquinta, Mariano 1947- Modica, Giuseppe 1948-
author_GND	(DE-588)111595738 (DE-588)133455777
author_facet	Giaquinta, Mariano 1947- Modica, Giuseppe 1948-
author_role	aut aut
author_sort	Giaquinta, Mariano 1947-
author_variant	m g mg g m gm
building	Verbundindex
bvnumber	BV023356538
callnumber-first	Q - Science
callnumber-label	QA184
callnumber-raw	QA184.2
callnumber-search	QA184.2
callnumber-sort	QA 3184.2
callnumber-subject	QA - Mathematics
classification_rvk	SK 130
ctrlnum	(OCoLC)123954872 (DE-599)BVBBV023356538
dewey-full	515
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	515 - Analysis
dewey-raw	515
dewey-search	515
dewey-sort	3515
dewey-tens	510 - Mathematics
discipline	Mathematik
format	Book
fullrecord	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02006nam a2200553 c 4500</leader><controlfield tag="001">BV023356538</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20080820 </controlfield><controlfield tag="007">t\|</controlfield><controlfield tag="008">080623s2007 xx ad\|\| \|\|\|\| 00\|\|\| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780817643744</subfield><subfield code="9">978-0-8176-4374-4</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0817643745</subfield><subfield code="9">0-8176-4374-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)123954872</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV023356538</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA184.2</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 130</subfield><subfield code="0">(DE-625)143216:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Giaquinta, Mariano</subfield><subfield code="d">1947-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)111595738</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Mathematical analysis</subfield><subfield code="b">linear and metric structures and continuity</subfield><subfield code="c">Mariano Giaquinta ; Giuseppe Modica</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boston [u.a.]</subfield><subfield code="b">Birkhäuser</subfield><subfield code="c">2007</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVIII, 465 S.</subfield><subfield code="b">Ill., graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algèbre linéaire</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Analyse fonctionnelle</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Análise funcional</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Continu (Mathématiques)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Espaces vectoriels</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fonctions (Mathématiques)</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Lineaire algebra</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Matrizes (álgebra) (teoria)</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Ruimten (wiskunde)</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Topologie</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Álgebra linear</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Algebras, Linear</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Continuum (Mathematics)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functional analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functions</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Vector spaces</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Analysis</subfield><subfield code="0">(DE-588)4001865-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Analysis</subfield><subfield code="0">(DE-588)4001865-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Modica, Giuseppe</subfield><subfield code="d">1948-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)133455777</subfield><subfield code="4">aut</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Regensburg</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016540091&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-016540091</subfield></datafield></record></collection>
id	DE-604.BV023356538
illustrated	Illustrated
indexdate	2024-12-20T13:14:23Z
institution	BVB
isbn	9780817643744 0817643745
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-016540091
oclc_num	123954872
open_access_boolean
owner	DE-355 DE-BY-UBR
owner_facet	DE-355 DE-BY-UBR
physical	XVIII, 465 S. Ill., graph. Darst.
publishDate	2007
publishDateSearch	2007
publishDateSort	2007
publisher	Birkhäuser
record_format	marc
spellingShingle	Giaquinta, Mariano 1947- Modica, Giuseppe 1948- Mathematical analysis linear and metric structures and continuity Algèbre linéaire Analyse fonctionnelle Análise funcional larpcal Continu (Mathématiques) Espaces vectoriels Fonctions (Mathématiques) Lineaire algebra gtt Matrizes (álgebra) (teoria) larpcal Ruimten (wiskunde) gtt Topologie gtt Álgebra linear larpcal Algebras, Linear Continuum (Mathematics) Functional analysis Functions Vector spaces Analysis (DE-588)4001865-9 gnd
subject_GND	(DE-588)4001865-9
title	Mathematical analysis linear and metric structures and continuity
title_auth	Mathematical analysis linear and metric structures and continuity
title_exact_search	Mathematical analysis linear and metric structures and continuity
title_full	Mathematical analysis linear and metric structures and continuity Mariano Giaquinta ; Giuseppe Modica
title_fullStr	Mathematical analysis linear and metric structures and continuity Mariano Giaquinta ; Giuseppe Modica
title_full_unstemmed	Mathematical analysis linear and metric structures and continuity Mariano Giaquinta ; Giuseppe Modica
title_short	Mathematical analysis
title_sort	mathematical analysis linear and metric structures and continuity
title_sub	linear and metric structures and continuity
topic	Algèbre linéaire Analyse fonctionnelle Análise funcional larpcal Continu (Mathématiques) Espaces vectoriels Fonctions (Mathématiques) Lineaire algebra gtt Matrizes (álgebra) (teoria) larpcal Ruimten (wiskunde) gtt Topologie gtt Álgebra linear larpcal Algebras, Linear Continuum (Mathematics) Functional analysis Functions Vector spaces Analysis (DE-588)4001865-9 gnd
topic_facet	Algèbre linéaire Analyse fonctionnelle Análise funcional Continu (Mathématiques) Espaces vectoriels Fonctions (Mathématiques) Lineaire algebra Matrizes (álgebra) (teoria) Ruimten (wiskunde) Topologie Álgebra linear Algebras, Linear Continuum (Mathematics) Functional analysis Functions Vector spaces Analysis
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016540091&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT giaquintamariano mathematicalanalysislinearandmetricstructuresandcontinuity AT modicagiuseppe mathematicalanalysislinearandmetricstructuresandcontinuity

Verfügbarkeit

‌

Inhaltsverzeichnis