Spectral theory: basic concepts and applications
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Cham, Switzerland
Springer Nature Switzerland AG
[2020]
|
| Schriftenreihe: | Graduate texts in mathematics
284 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032709317&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | x, 338 Seiten Illustrationen |
| ISBN: | 9783030380014 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1819281532778446848 |
|---|---|
| adam_text | Contents 1 Introduction......................................................................................................... 1 2 Hilbert Spaces..................................................................................................... 5 5 7 9 15 18 24 27 31 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 Normed Vector Spaces........................................................................... Lp Spaces................................................................................................ Bounded Linear Maps............................................................................ Hilbert Spaces......................................................................................... Sobolev Spaces....................................................................................... Orthogonality.......................................................................................... Orthonormal Bases................................................................................. Exercises.................................................................................................. 3 Operators............................................................................................................. 3.1 3.2 3.3 3.4 3.5 3.6 Unbounded Operators............................................................................ Adjoints................................................................................................... Closed Operators.................................................................................... Symmetry and Self-
adjointness............................................................. Compact Operators................................................................................. Exercises.................................................................................................. 4 Spectrum and Resolvent .................................................................................. 4.1 4.2 4.3 4.4 4.5 5 Definitions and Examples...................................................................... Resolvent ................................................................................................ Spectrum of Self-adjoint Operators....................................................... Spectral Theory of Compact Operators ............................................... Exercises.................................................................................................. 35 35 37 41 47 57 62 67 67 79 86 89 96 101 Unitary Operators ................................................................................... 102 The Main Theorem................................................................................. 107 Functional Calculus............................................................................... 112 Spectral Decomposition......................................................................... 115 Exercises.................................................................................................. 121 The Spectral Theorem....................................................................................... 5.1 5.2 5.3 5.4 5.5 ix
Contents x 6 The Laplacian with Boundary Conditions.................................................. 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 125 Self-adjoint Extensions........................................................................... 129 Discreteness of Spectrum...................................................................... 135 Regularity of Eigenfunctions................................................................ 143 Eigenvalue Computations...................................................................... 147 Asymptotics of Dirichlet Eigenvalues.................................................. 155 Nodal Domains....................................................................................... 171 Isoperimetric Inequalities and Minimal Eigenvalues.......................... 174 Exercises.................................................................................................. 179 7 Schrôdinger Operators..................................................................................... 7.1 7.2 7.3 7.4 7.5 7.6 7.7 Positive Potentials.................................................................................. Relatively Bounded Perturbations......................................................... Relatively Compact Perturbations......................................................... Hydrogen Atom ..................................................................................... Semiclassical Asymptotics..................................................................... Periodic
Potentials.................................................................................. Exercises.................................................................................................. 183 184 194 197 203 207 214 220 8 Operators on Graphs......................................................................................... 225 Combinatorial Laplacians...................................................................... Quantum Graphs...................................................................................... Spectral Properties of Compact Quantum Graphs............................... Eigenvalue Comparison......................................................................... Eigenvalue Asymptotics......................................................................... Exercises.................................................................................................. 226 230 232 234 237 242 9 Spectral Theory on Manifolds......................................................................... 245 245 250 262 266 270 282 287 291 298 8.1 8.2 8.3 8.4 8.5 8.6 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 Smooth Manifolds................................................................................... Riemannian Metrics............................................................................... The Laplacian.......................................................................................... Spectrum of a Compact Manifold......................................................... Heat
Equation.......................................................................................... Wave Propagation on Compact Manifolds........................................... Complete Manifolds and Essential Self-adjointness........................... Essential Spectrum of Complete Manifolds......................................... Exercises.................................................................................................. 303 Measure and Integration ........................................................................ 303 Lp Spaces................................................................................................ 315 Fourier Transform.................................................................................. 320 Elliptic Regularity.................................................................................. 324 A Background Material........................................................................................ A. 1 A.2 A.3 A.4 References................................................................................................................... 331 Index............................................................................................................................. 335
|
| any_adam_object | 1 |
| author | Borthwick, David |
| author_GND | (DE-588)1112155821 |
| author_facet | Borthwick, David |
| author_role | aut |
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| building | Verbundindex |
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| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.353 |
| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV047306263 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T19:15:41Z |
| institution | BVB |
| isbn | 9783030380014 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-032709317 |
| oclc_num | 1151827906 |
| open_access_boolean | |
| owner | DE-11 DE-19 DE-BY-UBM DE-739 |
| owner_facet | DE-11 DE-19 DE-BY-UBM DE-739 |
| physical | x, 338 Seiten Illustrationen |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | Springer Nature Switzerland AG |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spellingShingle | Borthwick, David Spectral theory basic concepts and applications Graduate texts in mathematics Partial Differential Equations Operator Theory Functional Analysis Partial differential equations Operator theory Functional analysis Spektraltheorie (DE-588)4116561-5 gnd Unbeschränkter Operator (DE-588)4236037-7 gnd Hilbert-Raum (DE-588)4159850-7 gnd Differentialoperator (DE-588)4012251-7 gnd |
| subject_GND | (DE-588)4116561-5 (DE-588)4236037-7 (DE-588)4159850-7 (DE-588)4012251-7 |
| title | Spectral theory basic concepts and applications |
| title_auth | Spectral theory basic concepts and applications |
| title_exact_search | Spectral theory basic concepts and applications |
| title_full | Spectral theory basic concepts and applications David Borthwick |
| title_fullStr | Spectral theory basic concepts and applications David Borthwick |
| title_full_unstemmed | Spectral theory basic concepts and applications David Borthwick |
| title_short | Spectral theory |
| title_sort | spectral theory basic concepts and applications |
| title_sub | basic concepts and applications |
| topic | Partial Differential Equations Operator Theory Functional Analysis Partial differential equations Operator theory Functional analysis Spektraltheorie (DE-588)4116561-5 gnd Unbeschränkter Operator (DE-588)4236037-7 gnd Hilbert-Raum (DE-588)4159850-7 gnd Differentialoperator (DE-588)4012251-7 gnd |
| topic_facet | Partial Differential Equations Operator Theory Functional Analysis Partial differential equations Operator theory Functional analysis Spektraltheorie Unbeschränkter Operator Hilbert-Raum Differentialoperator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032709317&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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