Availability: Introduction to functional analysis with applications

Introduction to functional analysis with applications:

Saved in:

Bibliographic Details
Main Author:	Siddiqi, Abul Hasan (Author)
Format:	Book
Language:	English
Published:	Tunbridge Wells [u.a.] Anshan [u.a.] 2006
Subjects:	Functional analysis Functional equations Funktionalanalysis Einführung
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016091586&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Item Description:	Literaturverz. S. [351] - 358
Physical Description:	XVII, 362 S. graph. Darst. 25 cm
ISBN:	1904798918

Staff View

MARC


LEADER	00000nam a2200000 c 4500
001	BV022886684
003	DE-604
005	20080717
007	t\|
008	071017s2006 xx d\|\|\| \|\|\|\| 00\|\|\| eng d
020			\|a 1904798918 \|c (cased) \|9 1-904798-91-8
035			\|a (OCoLC)85689430
035			\|a (DE-599)GBV525505032
040			\|a DE-604 \|b ger \|e aacr
041	0		\|a eng
049			\|a DE-703
050		0	\|a QA320
082	0		\|a 515.7 \|2 22
084			\|a SK 600 \|0 (DE-625)143248: \|2 rvk
100	1		\|a Siddiqi, Abul Hasan \|e Verfasser \|4 aut
245	1	0	\|a Introduction to functional analysis with applications \|c A. H. Siddiqi, Khalil Ahmad, P. Manchanda
246	1	3	\|a Functional analysis with applications
264		1	\|a Tunbridge Wells [u.a.] \|b Anshan [u.a.] \|c 2006
300			\|a XVII, 362 S. \|b graph. Darst. \|c 25 cm
336			\|b txt \|2 rdacontent
337			\|b n \|2 rdamedia
338			\|b nc \|2 rdacarrier
500			\|a Literaturverz. S. [351] - 358
650		4	\|a Functional analysis
650		4	\|a Functional equations
650	0	7	\|a Funktionalanalysis \|0 (DE-588)4018916-8 \|2 gnd \|9 rswk-swf
655		7	\|0 (DE-588)4151278-9 \|a Einführung \|2 gnd-content
689	0	0	\|a Funktionalanalysis \|0 (DE-588)4018916-8 \|D s
689	0		\|5 DE-604
700	1		\|a Ahmad, Khalil \|e Sonstige \|4 oth
700	1		\|a Manchanda, Pammy \|e Sonstige \|4 oth
856	4	2	\|m GBV Datenaustausch \|q application/pdf \|u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016091586&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA \|3 Inhaltsverzeichnis
943	1		\|a oai:aleph.bib-bvb.de:BVB01-016091586

Record in the Search Index

_version_	1819340348508340224
adam_text	INTRODUCTION TO FUNCTIONAL ANALYSIS WITH APPLICATIONS A.H. SIDDIQI KHALIL AHMAD P. MANCHANDA TUNBRIDGE WELLS, UK ANAMAYA PUBLISHERS NEW DELHI CONTENTS PREFACE VII LIST OF SYMBOLS .: - IX 1. NORMED AND BANACH SPACES 1 1.1 BASIC DEFINITIONS AND PROPERTIES 1 1.2 EXAMPLES OF NORMED SPACES AND RELATED CONCEPTS 6 NORMED SPACES 6 BANACH SPACES 13 DIMENSION OF NORMED SPACES 13 OPEN AND CLOSED SPHERES 13 NORMED SUBSPACES 16 COMPLETION OF NORMED SPACES 16 ISOMETRY AND ISOMORPHISM 16 1.3 OPERATORS AND FUNCTIONALS 17 DEFINITIONS AND EXAMPLES 17 PROPERTIES OF LINEAR OPERATORS AND DUAL SPACE 25 ALGEBRA OF OPERATORS 32 1.4 CONVEX FUNCTIONALS (REAL-VALUED CONVEX FUNCTIONS ON NORMED SPACES) 38 CONVEX SETS 38 AFFINE OPERATOR 40 CONVEX FUNCTIONALS 40 LOWER SEMICONTINUOUS (LSC) AND UPPER SEMICONTINUOUS (USE) FUNCTIONALS 43 1.5 TOPOLOGICAL PROPERTIES OF NORMED SPACES 44 COMPACTNESS IN NORMED SPACES 44 SEPARABILITY AND CONNECTEDNESS FOR NORMED SPACES 49 EQUIVALENT NORMS AND FINITE-DIMENSIONAL SPACES SO REFLEXIVE NORMED SPACES AND DIFFERENT KINDS OF TOPOLOGIES 53 NORME D SPACES WITH BASIS OR BASE 54 1.6 GEOMETRICAL PROPERTIES OF NORMED SPACES 55 1.7 SOME MORE EXAMPLES 56 EXERCISES 75 SOLUTIONS TO EXERCISES 77 2. INNER PRODUCT AND HILBERT SPACES : 81 2.1 BASIC DEFINITIONS AND PROPERTIES 81 DEFINITIONS, EXAMPLES AND PROPERTIES OF INNER-PRODUCT SPACE 81 XIV CONTENTS HILBERT SPACE 86 PARALLELOGRAM LAW AND CHARACTERIZATION OF HILBERT SPACE 87 2.2 ORTHOGONAL COMPLEMENTS AND PROJECTION THEOREM 93 ORTHOGONAL COMPLEMENTS AND PROJECTIONS 93 PROJECTION THEOREM 95 2.3 ORTHONORMAL SYSTEMS AND FOURIER EXPANSION 100 DEFINITIONS, EXAMPLES AND GRAM-SCHMIDT ORTHOGONALIZATION -** PROCESS 100 BESSEL S INEQUALITY 104 2.4 DUALITY AND REFLEXIVITY 106 RIESZ REPRESENTATION THEOREM 106 REFLEXIVITY OF HILBERT SPACES 109 2.5 OPERATORS IN HILBERT SPACE 110 ADJOINT OF A BOUNDED LINEAR OPERATOR ON A HILBERT SPACE 110 SELF-ADJOINT, POSITIVE, NORMAL AND UNITARY OPERATORS 115 ADJOINT OF AN UNBOUNDED LINEAR OPERATOR 122 2.6 BILINEAR FORMS AND LAX-MILGRARRI LEMMA 124 2.7 PROJECTION ON CONVEX SETS 131 2.8 SOME MORE EXAMPLES 134 EXERCISES 144 SOLUTIONS TO EXERCISES 146 3. FUNDAMENTAL THEOREMS 149 3.1 EXTENSION FORM OF THE HAHN-BANACH THEOREM AND ITS CONSEQUENCES 149 CONSEQUENCES OF THE EXTENSION FORM OF THE HAHN-BANACH THEOREM 154 3.2 GEOMETRIC FORM OF THE HAHN-BANACH THEOREM AND ITS COROLLARIES 157 3.3 PRINCIPLE OF UNIFORM BOUNDEDNESS AND ITS APPLICATIONS 159 PRINCIPLE OF UNIFORM BOUNDEDNESS 159 APPLICATIONS OF THE PRINCIPLE OF UNIFORM BOUNDEDNESS IN FOURIER ANALYSIS 160 3.4 OPEN MAPPING AND CLOSED GRAPH THEOREMS 162 GRAPH OF A LINEAR OPERATOR AND CLOSEDNESS PROPERTY 162 OPEN MAPPING THEOREM 164 CLOSED GRAPH THEOREM 165 3.5 EXAMPLES 166 EXERCISES 168 SOLUTIONS TO EXERCISES 169 4. WEAK TOPOLOGIES, WEAK CONVERGENCE AND REFLEXIVE SPACES 170 4.1 WEAK TOPOLOGIES 170 4.2 WEAK CONVERGENCE 171 4.3 REFLEXIVE BANACH SPACES 173 : CONTENTS XV 4.4 WEAK CONVERGENCE IN HILBERT SPACES 174 4.5 EXAMPLES 176 EXERCISES 178 SOLUTIONS TO EXERCISES 178 5. DIFFERENTIATION AND INTEGRATION IN NORMED SPACES 180 5.1 GATEAUX DERIVATIVE 180 5.2 FRECHET DERIVATIVE 183 5.3 SUBDIFFERENTIAL 186 5.4 INTEGRATION IN NORMED SPACES 188 EXERCISES 189 SOLUTIONS TO EXERCISES 190 6. FIXED-POINT THEOREMS AND THEIR APPLICATIONS 191 6.1 BANACH CONTRACTION PRINCIPLE AND ITS GENERALIZATIONS 191 6.2 SCHAUDER S FIXED-POINT THEOREM 195 6.3 APPLICATIONS OF BANACH CONTRACTION PRINCIPLE 196 APPLICATION TO MATRIX EQUATION 196 APPLICATION TO DIFFERENTIAL EQUATIONS 201 EXERCISES 203 SOLUTIONS TO EXERCISES 206 7. RUDIMENTS OF SPECTRAL THEORY 210 7.1 SPECTRAL PROPERTIES OF BOUNDED LINEAR OPERATORS 210 7.2 COMPACT OPERATORS 211 7.3 SPECTRAL PROPERTIES OF SELF-ADJOINT AND COMPACT OPERATORS 215 7.4 SPECTRAL DECOMPOSITION 216 SOLVABILITY OF OPERATOR EQUATIONS 219 CHARACTERIZATION OF SOLVABILITY IN TERMS OF RANGE AND NULL SPACES 222 CHARACTERIZATION OF LAX-MILGRAM LEMMA 223 EXISTENCE THEOREM FOR NONLINEAR OPERATORS 224 7.5 EXAMPLES 225 EXERCISES 226 SOLUTIONS TO EXERCISES 227 8. BOUNDARY VALUE PROBLEMS 230 8.1 DEFINITION AND EXAMPLES OF BOUNDARY VALUE PROBLEMS 230 DEFINITION 230 EXAMPLES OF BVPS 231 8.2 ABSTRACT EQUATIONS 236 8.3 SOBOLEV SPACE 238 EXAMPLES OF DISTRIBUTION 239 8.4 CERTAIN REMARKS CONCERNING THE SOLUTIONS OF BVPS 246 XVI CONTENTS EXERCISES 249 SOLUTIONS TO EXERCISES 249 9. OPTIMIZATION 251 9.1 MINIMIZATION OF FUNCTIONALS 251 9.2 CALCULUS OF VARIATION AND LINEAR PROGRAMMING -255 CALCULUS OF VARIATION 255 LINEAR PROGRAMMING 257 EXERCISES 257 SOLUTIONS TO EXERCISES 258 10. VARIATIONAL INEQUALITIES 260 10.1 LIONS-STAMPACCHIA THEORY 260 10.2 PHYSICAL PHENOMENA REPRESENTED BY VARIATIONAL INEQUALITIES 265 EXERCISES 267 SOLUTIONS TO EXERCISES 267 11. THE FINITE-ELEMENT METHOD 269 11.1 APPROXIMATE PROBLEM 270 11.2 INTERNAL APPROXIMATION OF// (Q) 273 11.3 FINITE ELEMENTS 275 11.4 APPLICATION OF THE FINITE-ELEMENT METHOD TO SOLVE BOUNDARY VALUE PROBLEMS 279 PRACTICAL METHOD TO COMPUTE A(WJ, W,) 281 11.5 EFFECT OF NUMERICAL INTEGRATION 281 11.6 ABSTRACT ERROR ESTIMATE FOR THE NONCONFORMING FINITE-ELEMENT METHOD 284 11.7 ABSTRACT ERROR ESTIMATION FOR VARIATIONAL INEQUALITIES 285 EXERCISES 286 SOLUTIONS TO EXERCISES 287 12. OPTIMAL CONTROL 288 12.1 PROBLEM ILLUSTRATION WITH THE HELP OF AN EXAMPLE AND FORMULATION OF GENERAL PROBLEM 289 FORMULATION OF THE GENERAL OPTIMAL CONTROL PROBLEM FOR A SYSTEM REPRESENTED BY DIFFERENTIAL EQUATION 290 12.2 LINEAR QUADRATIC CONTROL PROBLEM 291 EXERCISES 297 SOLUTIONS TO EXERCISES 297 13. WAVELETS 298 13.1 RECAPITULATION OF SOME BASIC CONCEPTS 298 13.2 CONTINUOUS WAVELET TRANSFORM 300 CONTENTS XVII 13.3 EXAMPLES OF WAVELETS 301 13.4 DECAY OF CONTINUOUS WAVELET TRANSFORM 308 13.5 MULTIRESOLUTION ANALYSIS 310 EXAMPLES OF MULTIRESOLUTION ANALYSIS 311 IMPORTANT PROPERTIES OF MRA 311 13.6 DECOMPOSITION AND RECONSTRUCTION ALGORITHMS 319 13.7 BESTAF-TERMAPPROXIMATION 320 13.8 WAVELET AND FUNCTION SPACES 322 EXERCISES 322 APPENDIX A 325 APPENDIX B 328 APPENDIX C 331 APPENDIX D 335 APPENDIX E 343 APPENDIX F 345 REFERENCES 351 INDEX 359
any_adam_object	1
author	Siddiqi, Abul Hasan
author_facet	Siddiqi, Abul Hasan
author_role	aut
author_sort	Siddiqi, Abul Hasan
author_variant	a h s ah ahs
building	Verbundindex
bvnumber	BV022886684
callnumber-first	Q - Science
callnumber-label	QA320
callnumber-raw	QA320
callnumber-search	QA320
callnumber-sort	QA 3320
callnumber-subject	QA - Mathematics
classification_rvk	SK 600
ctrlnum	(OCoLC)85689430 (DE-599)GBV525505032
dewey-full	515.7
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	515 - Analysis
dewey-raw	515.7
dewey-search	515.7
dewey-sort	3515.7
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>01596nam a2200421 c 4500</leader><controlfield tag="001">BV022886684</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20080717 </controlfield><controlfield tag="007">t\|</controlfield><controlfield tag="008">071017s2006 xx d\|\|\| \|\|\|\| 00\|\|\| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1904798918</subfield><subfield code="c">(cased)</subfield><subfield code="9">1-904798-91-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)85689430</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)GBV525505032</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA320</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.7</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 600</subfield><subfield code="0">(DE-625)143248:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Siddiqi, Abul Hasan</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Introduction to functional analysis with applications</subfield><subfield code="c">A. H. Siddiqi, Khalil Ahmad, P. Manchanda</subfield></datafield><datafield tag="246" ind1="1" ind2="3"><subfield code="a">Functional analysis with applications</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Tunbridge Wells [u.a.]</subfield><subfield code="b">Anshan [u.a.]</subfield><subfield code="c">2006</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVII, 362 S.</subfield><subfield code="b">graph. Darst.</subfield><subfield code="c">25 cm</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="500" ind1=" " ind2=" "><subfield code="a">Literaturverz. S. [351] - 358</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functional analysis</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Functional equations</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Funktionalanalysis</subfield><subfield code="0">(DE-588)4018916-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4151278-9</subfield><subfield code="a">Einführung</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Funktionalanalysis</subfield><subfield code="0">(DE-588)4018916-8</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">Ahmad, Khalil</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Manchanda, Pammy</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">GBV Datenaustausch</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=016091586&sequence=000001&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:BVB01-016091586</subfield></datafield></record></collection>
genre	(DE-588)4151278-9 Einführung gnd-content
genre_facet	Einführung
id	DE-604.BV022886684
illustrated	Illustrated
indexdate	2024-12-20T13:05:27Z
institution	BVB
isbn	1904798918
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-016091586
oclc_num	85689430
open_access_boolean
owner	DE-703
owner_facet	DE-703
physical	XVII, 362 S. graph. Darst. 25 cm
publishDate	2006
publishDateSearch	2006
publishDateSort	2006
publisher	Anshan [u.a.]
record_format	marc
spellingShingle	Siddiqi, Abul Hasan Introduction to functional analysis with applications Functional analysis Functional equations Funktionalanalysis (DE-588)4018916-8 gnd
subject_GND	(DE-588)4018916-8 (DE-588)4151278-9
title	Introduction to functional analysis with applications
title_alt	Functional analysis with applications
title_auth	Introduction to functional analysis with applications
title_exact_search	Introduction to functional analysis with applications
title_full	Introduction to functional analysis with applications A. H. Siddiqi, Khalil Ahmad, P. Manchanda
title_fullStr	Introduction to functional analysis with applications A. H. Siddiqi, Khalil Ahmad, P. Manchanda
title_full_unstemmed	Introduction to functional analysis with applications A. H. Siddiqi, Khalil Ahmad, P. Manchanda
title_short	Introduction to functional analysis with applications
title_sort	introduction to functional analysis with applications
topic	Functional analysis Functional equations Funktionalanalysis (DE-588)4018916-8 gnd
topic_facet	Functional analysis Functional equations Funktionalanalysis Einführung
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016091586&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT siddiqiabulhasan introductiontofunctionalanalysiswithapplications AT ahmadkhalil introductiontofunctionalanalysiswithapplications AT manchandapammy introductiontofunctionalanalysiswithapplications AT siddiqiabulhasan functionalanalysiswithapplications AT ahmadkhalil functionalanalysiswithapplications AT manchandapammy functionalanalysiswithapplications

Availability

‌

Order via interlibrary loan Table of Contents