Verfügbarkeit: Distributions and operators | Technische Universität München

Distributions and operators:

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Bibliographische Detailangaben
Beteilige Person:	Grubb, Gerd 1939- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York, NY Springer 2009
Schriftenreihe:	Graduate texts in mathematics 252
Schlagwörter:	Hilbert, Espace de Théorie des distributions (Analyse fonctionnelle) Théorie des opérateurs Hilbert space Operator theory Theory of distributions (Functional analysis) Distributionstheorie Distribution > Funktionalanalysis Pseudodifferentialoperator Lehrbuch
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016994351&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XII, 461 S. graph. Darst. 235 mm x 155 mm
ISBN:	9780387848945

Internformat

MARC


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Datensatz im Suchindex

DE-BY-TUM_call_number	0102 MAT 470f 2011 A 7180
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adam_text	Contents Preface ....................................................... v Part I Distributions and derivatives 1 Motivation and overview ................................. 3 1.1 Introduction ........................................... 3 1.2 On the definition of distributions ......................... 6 2 Function spaces and approximation ....................... 9 2.1 The space of test functions .............................. 9 2.2 Some other function spaces .............................. 16 2.3 Approximation theorems ................................ 17 2.4 Partitions of unity ...................................... 23 Exercises for Chapter 2...................................... 24 3 Distributions. Examples and rules of calculus ............. 27 3.1 Distributions ........................................... 27 3.2 Rules of calculus for distributions ......................... 31 3.3 Distributions with compact support ....................... 36 3.4 Convolutions and coordinate changes ..................... 40 3.5 The calculation rules and the weak* topology on 3 ........ 46 Exercises for Chapter 3...................................... 50 Part II Extensions and applications 4 Realizations and Sobolev spaces ..........,............... 57 4.1 Realizations of differential operators ...................... 57 4.2 Sobolev spaces ......................................... 61 4.3 The one-dimensional case ................................ 68 4.4 Boundary value problems in higher dimensions ............. 77 Exercises for Chapter 4...................................... 86 x Contents 5 Fourier transformation of distributions ................... 05 5.1 Rapidly decreasing functions ............................. 95 5.2 Temperate distributions .................................103 5.3 The Fourier transform on З ............................105 5.4 Homogeneity ...........................................110 5.5 Application to the Laplace operator .......................114 5.6 Distributions associated with nonintegrable functions .......116 Exercises for Chapter 5......................................120 6 Applications to differential operators. The Sobolev theorem 123 6.1 Differential and pseudodifferential operators on R™ .........123 6.2 Sobolev spaces of arbitrary real order. The Sobolev theorem . 127 6.3 Dualities between Sobolev spaces. The Structure theorem .... 132 6.4 Regularity theory for elliptic differential equations ..........138 Exercises for Chapter 6......................................144 Miscellaneous exercises (exam problems) .......................147 Part III Pseudodifferential operators 7 Pseudodifferential operators on open sets .................163 7.1 Symbols and operators, mapping properties ................ 163 7.2 Negligible operators ..................................... 172 7.3 Composition rules ...................................... 178 7.4 Elliptic pseudodifferential operators ....................... 183 7.5 Strongly elliptic operators, the Gårding inequality .......... 189 Exercises for Chapter 7...................................... 193 8 Pseudodifferential operators on manifolds, index of elliptic operators .........................................195 8.1 Coordinate changes .....................................195 8.2 Operators on manifolds .................................197 8.3 Fredholm theory, the index ..............................208 Exercises for Chapter 8......................................215 Part IV Boundary value problems 9 Boundary value problems in a constant-coefficient case ... 219 9.1 Boundary maps for the half-space ........................219 9.2 The Dirichlet problem for I - Δ on the half-space ..........228 9.3 The Neumann problem for I — Δ on the half-space .........234 9.4 Other realizations of I - A ..............................236 9.5 Variable-coefficient cases, higher orders, systems ............ 24(i Exercises for Chapter 9......................................248 Contents xi 10 Pseudodifferential boundary operators ....................251 10.1 The real formulation ....................................251 10.2 Fourier transform and Laguerre expansion of <5^+ ...........266 10.3 The complex formulation ................................275 10.4 Composition rules ......................................281 10.5 Continuity .............................................289 10.6 Elliptic ^dbo s .........................................296 Exercises for Chapter 10.....................................300 11 Pseudodifferential methods for boundary value problems . 305 11.1 The Calderón projector .................................305 11.2 Application to boundary value problems ...................317 11.3 The solution operator for the Dirichlet problem ............320 Exercises for Chapter 11.....................................326 Part V Topics on Hubert space operators 12 Unbounded linear operators ..............................337 12.1 Unbounded operators in Banach spaces ...................337 12.2 Unbounded operators in Hubert spaces ....................340 12.3 Symmetric, selfadjoint and semibounded operators ..........343 12.4 Operators associated with sesquilinear forms ...............350 12.5 The Friedrichs extension ................................359 12.6 More on variational operators ............................361 Exercises for Chapter 12.....................................364 13 Families of extensions .....................................373 13.1 A universal parametrization of extensions ..................373 13.2 The symmetric case .....................................383 13.3 Consequences for resolvents ..............................393 13.4 Boundary triplets and M-functions .......................397 Exercises for Chapter 13.....................................402 14 Semigroups of operators ..................................405 14.1 Evolution equations .....................................405 14.2 Contraction semigroups in Banach spaces ..................409 14.3 Contraction semigroups in Hubert spaces ..................416 14.4 Applications ...........................................419 Exercises for Chapter 14.....................................421 A Some notation and prerequisites ..........................423 Exercises for Appendix A ....................................429 xii Contents В Topological vector spaces ................................. 431 B.I Fréchet spaces ......................................... 431 В. 2 Inductive limits of Fréchet spaces ......................... 441 Exercises for Appendix В .................................... 443 С Function spaces on sets with smooth boundary ...........447 Exercises for Appendix G ....................................450 Bibliography ..................................................451 Index .........................................................457
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author	Grubb, Gerd 1939-
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id	DE-604.BV035187673
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isbn	9780387848945
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-016994351
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owner	DE-384 DE-706 DE-355 DE-BY-UBR DE-20 DE-19 DE-BY-UBM DE-83 DE-824 DE-11 DE-188 DE-91G DE-BY-TUM
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physical	XII, 461 S. graph. Darst. 235 mm x 155 mm
publishDate	2009
publishDateSearch	2009
publishDateSort	2009
publisher	Springer
record_format	marc
series	Graduate texts in mathematics
series2	Graduate texts in mathematics
spellingShingle	Grubb, Gerd 1939- Distributions and operators Graduate texts in mathematics Hilbert, Espace de Théorie des distributions (Analyse fonctionnelle) Théorie des opérateurs Hilbert space Operator theory Theory of distributions (Functional analysis) Distributionstheorie (DE-588)4150254-1 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd Pseudodifferentialoperator (DE-588)4047640-6 gnd
subject_GND	(DE-588)4150254-1 (DE-588)4070505-5 (DE-588)4047640-6 (DE-588)4123623-3
title	Distributions and operators
title_auth	Distributions and operators
title_exact_search	Distributions and operators
title_full	Distributions and operators Gerd Grubb
title_fullStr	Distributions and operators Gerd Grubb
title_full_unstemmed	Distributions and operators Gerd Grubb
title_short	Distributions and operators
title_sort	distributions and operators
topic	Hilbert, Espace de Théorie des distributions (Analyse fonctionnelle) Théorie des opérateurs Hilbert space Operator theory Theory of distributions (Functional analysis) Distributionstheorie (DE-588)4150254-1 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd Pseudodifferentialoperator (DE-588)4047640-6 gnd
topic_facet	Hilbert, Espace de Théorie des distributions (Analyse fonctionnelle) Théorie des opérateurs Hilbert space Operator theory Theory of distributions (Functional analysis) Distributionstheorie Distribution Funktionalanalysis Pseudodifferentialoperator Lehrbuch
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016994351&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000000067
work_keys_str_mv	AT grubbgerd distributionsandoperators

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