On spectral theory of elliptic operators:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
1996
|
| Series: | Operator theory
89 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 319 - 325 |
| Physical Description: | X, 328 S. |
| ISBN: | 3764353902 0817653902 |
Staff View
MARC
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| 100 | 1 | |a Egorov, Jurij V. |d 1938- |e Verfasser |0 (DE-588)121177181 |4 aut | |
| 245 | 1 | 0 | |a On spectral theory of elliptic operators |c Yuri Egorov ; Vladimir Kondratiev |
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 1996 | |
| 300 | |a X, 328 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Operator theory |v 89 | |
| 500 | |a Literaturverz. S. 319 - 325 | ||
| 650 | 4 | |a Spektraltheorie - Elliptischer Differentialoperator | |
| 650 | 0 | 7 | |a Elliptischer Differentialoperator |0 (DE-588)4140057-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Spektraltheorie |0 (DE-588)4116561-5 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Elliptischer Differentialoperator |0 (DE-588)4140057-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Kondrat'ev, Vladimir |e Verfasser |4 aut | |
| 830 | 0 | |a Operator theory |v 89 |w (DE-604)BV000000970 |9 89 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface IX
1 HUbert Spaces
1.1 Definition and basic properties 1
1.2 Examples 3
1.3 Orthonormal base 5
1.4 Fourier series 6
1.5 Subspaces, orthogonal sums 8
1.6 Linear functional 9
1.7 Weak convergence 11
1.8 Linear operators 15
1.9 Adjoint operators 16
1.10 The spectrum of an operator 17
1.11 Compact operators 18
1.12 Compact self adjoint operators 19
1.13 Integral operators 21
1.14 The Lax Milgram theorem 23
2 Functional Spaces
2.1 Notation and definitions 25
2.2 Lebesgue integral 27
2.3 Level sets of functions of a real variable 29
2.4 Symmetrization 32
2.5 The space Li(fi) 35
2.6 The space L2(fi) 36
2.7 The space LP(O), p 1 38
2.8 Density of the set of continuous functions in Li(n) 40
2.9 Density of the set of continuous functions in Lp(V,),p 1 41
2.10 Separability of LP(Q) 43
2.11 Global continuity of functions of Lp(fi) 44
2.12 Averaging 45
2.13 Compactness of a subset in LP(Q) 46
2.14 Fourier transform 47
VI Contents
2.15 The spaces Wâ„¢(0) 50
2.16 The averaging and generalized derivatives 54
2.17 Continuation of functions of Wâ„¢(fl) 56
2.18 The Sobolev integral representation 58
2.19 The space W^{ft,E) 58
2.20 Properties of the space W™O{£1) 59
2.21 Sobolev s embedding theorems 60
2.22 Poincare s inequality 61
2.23 Interpolation inequalities 68
2.24 Compactness of the embedding 70
2.25 Invariance of Wâ„¢(fl) under change of variables 72
2.26 The spaces Wâ„¢(n) for a smooth domain fl 73
2.27 The traces of functions of W^ (fi) 75
2.28 The space Hs 78
2.29 The traces of functions of W$(Rn) 83
2.30 The Hardy inequalities 89
2.31 The Morrey embedding theorem 105
3 Elliptic Operators
3.1 Strongly elliptic equations 109
3.2 Elliptic equations 115
3.3 Regularity of solutions 120
3.4 Boundary problems for elliptic equations 124
3.5 Smoothness of solutions up to boundary 130
4 Spectral Properties of Elliptic Operators
4.1 Variational principle 133
4.2 The spectrum of a self adjoint operator 139
4.3 The Friedrichs extension 143
4.4 Examples of linear unbounded operators 144
4.5 Self adjointness of the Schrodinger operator 148
5 The Sturm Liouville Problem
5.1 Elementary properties 153
5.2 On the first eigenvalue of a Sturm Liouville problem 170
5.3 On other estimates of the first eigenvalue 176
5.4 On a more general estimate of the first
eigenvalue of the Sturm Liouville operator 194
5.5 On estimates of all eigenvalues 202
6 Differential Operators of Any Order
6.1 Oscillation of solutions of an equation of any order 207
6.2 On estimates of the first eigenvalue for operators
of higher order 213
Contents VII
6.3 Introduction to a Lagrange problem 217
6.4 Preliminary estimates 220
6.5 Precise results 225
7 Eigenfunctions of Elliptic Operators in Bounded Domains
7.1 On the Dirichlet problem for strongly
elliptic equations 233
7.2 Estimates of eigenfunctions of strongly
elliptic operators 239
7.3 Equations of second order 242
7.4 Estimates of eigenfunctions of operator pencils 246
7.5 The method of stationary phase 248
7.6 Asymptotics of a fundamental solution of
an elliptic operator with constant coefficients 253
7.7 Estimates of the eigenfunctions of an elliptic
operator with constant coefficients 257
7.8 Estimates of the first eigenvalue of an elliptic
operator in a multi connected domain 265
7.9 Estimates of the first eigenvalue of the Schrodinger
operator in a bounded domain 271
8 Negative Spectra of Elliptic Operators
8.1 Introduction 275
8.2 One dimensional case 278
8.3 Some inequalities and embedding theorems 287
8.4 Estimates of the number of points of
the negative spectrum 294
8.5 Some generalizations 298
8.6 Lower estimates for the number TV 303
8.7 Other results 305
8.8 On moments of negative eigenvalues of
an elliptic operator 309
Bibliography 319
Index 327
|
| any_adam_object | 1 |
| author | Egorov, Jurij V. 1938- Kondrat'ev, Vladimir |
| author_GND | (DE-588)121177181 |
| author_facet | Egorov, Jurij V. 1938- Kondrat'ev, Vladimir |
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| author_sort | Egorov, Jurij V. 1938- |
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| building | Verbundindex |
| bvnumber | BV010789040 |
| classification_rvk | SK 620 |
| classification_tum | MAT 474f MAT 358f |
| ctrlnum | (OCoLC)246604956 (DE-599)BVBBV010789040 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010789040 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:58:56Z |
| institution | BVB |
| isbn | 3764353902 0817653902 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007207248 |
| oclc_num | 246604956 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-12 DE-19 DE-BY-UBM DE-706 DE-634 DE-11 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-12 DE-19 DE-BY-UBM DE-706 DE-634 DE-11 DE-188 |
| physical | X, 328 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Operator theory |
| series2 | Operator theory |
| spelling | Egorov, Jurij V. 1938- Verfasser (DE-588)121177181 aut On spectral theory of elliptic operators Yuri Egorov ; Vladimir Kondratiev Basel [u.a.] Birkhäuser 1996 X, 328 S. txt rdacontent n rdamedia nc rdacarrier Operator theory 89 Literaturverz. S. 319 - 325 Spektraltheorie - Elliptischer Differentialoperator Elliptischer Differentialoperator (DE-588)4140057-4 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 s Elliptischer Differentialoperator (DE-588)4140057-4 s DE-604 Kondrat'ev, Vladimir Verfasser aut Operator theory 89 (DE-604)BV000000970 89 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007207248&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Egorov, Jurij V. 1938- Kondrat'ev, Vladimir On spectral theory of elliptic operators Operator theory Spektraltheorie - Elliptischer Differentialoperator Elliptischer Differentialoperator (DE-588)4140057-4 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| subject_GND | (DE-588)4140057-4 (DE-588)4116561-5 |
| title | On spectral theory of elliptic operators |
| title_auth | On spectral theory of elliptic operators |
| title_exact_search | On spectral theory of elliptic operators |
| title_full | On spectral theory of elliptic operators Yuri Egorov ; Vladimir Kondratiev |
| title_fullStr | On spectral theory of elliptic operators Yuri Egorov ; Vladimir Kondratiev |
| title_full_unstemmed | On spectral theory of elliptic operators Yuri Egorov ; Vladimir Kondratiev |
| title_short | On spectral theory of elliptic operators |
| title_sort | on spectral theory of elliptic operators |
| topic | Spektraltheorie - Elliptischer Differentialoperator Elliptischer Differentialoperator (DE-588)4140057-4 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| topic_facet | Spektraltheorie - Elliptischer Differentialoperator Elliptischer Differentialoperator Spektraltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007207248&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000970 |
| work_keys_str_mv | AT egorovjurijv onspectraltheoryofellipticoperators AT kondratevvladimir onspectraltheoryofellipticoperators |