Heat kernels and spectral theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge u.a.
Cambridge Univ. Pr.
1989
|
| Edition: | 1. publ. |
| Series: | Cambridge tracts in mathematics
92 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | IX, 197 S. |
| ISBN: | 0521361362 0521409977 9780521409971 |
Staff View
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| 100 | 1 | |a Davies, Edward B. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Heat kernels and spectral theory |c E. B. Davies |
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| 264 | 1 | |a Cambridge u.a. |b Cambridge Univ. Pr. |c 1989 | |
| 300 | |a IX, 197 S. | ||
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| 650 | 7 | |a Elliptische differentiaalvergelijkingen |2 gtt | |
| 650 | 4 | |a Opérateurs elliptiques | |
| 650 | 7 | |a Spectraaltheorie |2 gtt | |
| 650 | 4 | |a Spectre (Mathématiques) | |
| 650 | 7 | |a Théorie spectrale (Mathématiques) |2 ram | |
| 650 | 4 | |a Équation de la chaleur | |
| 650 | 4 | |a Elliptic operators | |
| 650 | 4 | |a Heat equation | |
| 650 | 4 | |a Spectral theory (Mathematics) | |
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Record in the Search Index
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| adam_text | Contents
Preface vii
1 Introductory concepts 1
1.1 Some classical analysis 1
1.2 Quadratic forms 6
1.3 The Beurling Deny conditions 12
1.4 Symmetric Markov semigroups 21
1.5 An inequality of Hardy 25
1.6 Compactness and spectrum 35
1.7 Some Sobolev inequalities 40
1.8 Definition of Schrodinger operators 48
1.9 The asymptotic eigenvalue distribution 52
Notes 55
2 Logarithmic Sobolev inequalities 59
2.1 Contractivity properties 59
2.2 The fundamental inequalities 63
2.3 Examples and applications 71
2.4 Ultracontractivity, Sobolev and Nash inequalities 75
Notes 80
3 Gaussian bounds on heat kernels 82
3.1 Introduction 82
3.2 The upper bound 83
3.3 The lower bound
3.4 Functions of an elliptic operator 99
Notes 105
4 Boundary behaviour 107
4.1 Introduction 107
4.2 Transference to weighted L2 spaces 109
vi Contents
4.3 The harmonic oscillator 113
4.4 Rosen s lemma 117
4.5 Schrodinger operators 119
4.6 Elliptic operators on bounded regions 125
4.7 Singular elliptic operators 131
4.8 Potentials with local singularities 138
Notes 144
5 Riemannian manifolds 146
5.1 Fundamental properties of manifolds 146
5.2 Regularity properties of the heat equation 149
5.3 The parabolic Harnack inequality 157
5.4 Potential theory 164
5.5 Upper bound on the heat kernel 167
5.6 Lower bounds on the heat kernel 173
5.7 Hyperbolic space 176
Notes 183
References 187
Notation index 195
Index 196
|
| any_adam_object | 1 |
| author | Davies, Edward B. |
| author_facet | Davies, Edward B. |
| author_role | aut |
| author_sort | Davies, Edward B. |
| author_variant | e b d eb ebd |
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| bvnumber | BV001637318 |
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| ctrlnum | (OCoLC)17918566 (DE-599)BVBBV001637318 |
| dewey-full | 515.7/242 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7/242 |
| dewey-search | 515.7/242 |
| dewey-sort | 3515.7 3242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:33:25Z |
| institution | BVB |
| isbn | 0521361362 0521409977 9780521409971 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001072878 |
| oclc_num | 17918566 |
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| physical | IX, 197 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Cambridge Univ. Pr. |
| record_format | marc |
| series | Cambridge tracts in mathematics |
| series2 | Cambridge tracts in mathematics |
| spelling | Davies, Edward B. Verfasser aut Heat kernels and spectral theory E. B. Davies 1. publ. Cambridge u.a. Cambridge Univ. Pr. 1989 IX, 197 S. txt rdacontent n rdamedia nc rdacarrier Cambridge tracts in mathematics 92 Hier auch später erschienene, unveränderte Nachdrucke Differentiaaloperatoren gtt Elliptische differentiaalvergelijkingen gtt Opérateurs elliptiques Spectraaltheorie gtt Spectre (Mathématiques) Théorie spectrale (Mathématiques) ram Équation de la chaleur Elliptic operators Heat equation Spectral theory (Mathematics) Wärmeleitungsgleichung (DE-588)4188859-5 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Elliptischer Differentialoperator (DE-588)4140057-4 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 s Elliptischer Differentialoperator (DE-588)4140057-4 s DE-604 Wärmeleitungsgleichung (DE-588)4188859-5 s Cambridge tracts in mathematics 92 (DE-604)BV000000001 92 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001072878&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Davies, Edward B. Heat kernels and spectral theory Cambridge tracts in mathematics Differentiaaloperatoren gtt Elliptische differentiaalvergelijkingen gtt Opérateurs elliptiques Spectraaltheorie gtt Spectre (Mathématiques) Théorie spectrale (Mathématiques) ram Équation de la chaleur Elliptic operators Heat equation Spectral theory (Mathematics) Wärmeleitungsgleichung (DE-588)4188859-5 gnd Spektraltheorie (DE-588)4116561-5 gnd Elliptischer Differentialoperator (DE-588)4140057-4 gnd |
| subject_GND | (DE-588)4188859-5 (DE-588)4116561-5 (DE-588)4140057-4 |
| title | Heat kernels and spectral theory |
| title_auth | Heat kernels and spectral theory |
| title_exact_search | Heat kernels and spectral theory |
| title_full | Heat kernels and spectral theory E. B. Davies |
| title_fullStr | Heat kernels and spectral theory E. B. Davies |
| title_full_unstemmed | Heat kernels and spectral theory E. B. Davies |
| title_short | Heat kernels and spectral theory |
| title_sort | heat kernels and spectral theory |
| topic | Differentiaaloperatoren gtt Elliptische differentiaalvergelijkingen gtt Opérateurs elliptiques Spectraaltheorie gtt Spectre (Mathématiques) Théorie spectrale (Mathématiques) ram Équation de la chaleur Elliptic operators Heat equation Spectral theory (Mathematics) Wärmeleitungsgleichung (DE-588)4188859-5 gnd Spektraltheorie (DE-588)4116561-5 gnd Elliptischer Differentialoperator (DE-588)4140057-4 gnd |
| topic_facet | Differentiaaloperatoren Elliptische differentiaalvergelijkingen Opérateurs elliptiques Spectraaltheorie Spectre (Mathématiques) Théorie spectrale (Mathématiques) Équation de la chaleur Elliptic operators Heat equation Spectral theory (Mathematics) Wärmeleitungsgleichung Spektraltheorie Elliptischer Differentialoperator |
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