Expansions in eigenfunctions of selfadjoint operators:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
1968
|
| Series: | Translations of mathematical monographs
17 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | IX, 809 S. |
Staff View
MARC
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| 100 | 1 | |a Berezanskij, Jurij M. |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Razloženie po sobstvennym funkcijam samosoprjažennych operatorov |
| 245 | 1 | 0 | |a Expansions in eigenfunctions of selfadjoint operators |c by Ju. M. Berezanskiĭ |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 1968 | |
| 300 | |a IX, 809 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Translations of mathematical monographs |v 17 | |
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 4 | |a Spektraltheorie - Selbstadjungierter Operator | |
| 650 | 0 | 7 | |a Selbstadjungierter Operator |0 (DE-588)4180810-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Eigenfunktionenentwicklung |0 (DE-588)4151168-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Differentialgleichung |0 (DE-588)4012249-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Spektraltheorie |0 (DE-588)4116561-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Eigenfunktion |0 (DE-588)4151167-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Operator |0 (DE-588)4130529-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Differentialgleichung |0 (DE-588)4012249-9 |D s |
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| 689 | 1 | 1 | |a Selbstadjungierter Operator |0 (DE-588)4180810-1 |D s |
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| 689 | 2 | 0 | |a Operator |0 (DE-588)4130529-2 |D s |
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| 689 | 3 | 0 | |a Eigenfunktionenentwicklung |0 (DE-588)4151168-2 |D s |
| 689 | 3 | 1 | |a Selbstadjungierter Operator |0 (DE-588)4180810-1 |D s |
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Record in the Search Index
| _version_ | 1804117260866945024 |
|---|---|
| adam_text | TABLE OF CONTENTS
Page
Preface iii
Introduction 1
§1. Topological notions 1
§2. Integration 6
§3 Normed linear spaces and Hilbert spaces 9
§4. Classes of functions. Functional spaces 13
§5. The concept of Sobolev space 16
§6. The concept of imbedding theorems 17
§7. Some inequalities relating the Sobolev norm and the space W (G) 20
§8. The notion of a generalized function 22
§9. The notion of a generalized derivative in the sense of S. L.
Sobolev 24
§10. Averaging operators 26
§11. A second definition of a generalized derivative in the sense of
S. L. Sobolev, and a characterization of the elements of a
Sobolev space 28
Chapter I. Spaces with negative norms and generalized functions 31
§1. General theory of spaces with negative norms 32
§2. Tensor products and generalized kernels 39
§3 Examples of systems of generalized functions 50
§4. Equipment by means of linear topological spaces 66
Chapter II. Boundary value problems. General concepts 69
§1. General information concerning differential expressions 70
§2. The existence of solutions of the boundary value problem in the
space L2{G) 79
§3 Generalized solutions of boundary value problems 87
Chapter III. Boundary value problems and smooth generalized solutions
for elliptic equations. Green s function 103
§1. Lower estimates for quadratic forms on finite functions 103
vii
viii
§2. Boundary value problems for strongly elliptic equations. General¬
ized solutions 113
§3 Boundary value problems for elliptic equations. Smooth solutions 121
§4. Smoothness of solutions of elliptic equations 161
§5. Green s function 183
§6. Boundary value problems and smoothness of generalized solutions
up to the boundary for elliptic equations in the case of general
boundary conditions 204
Chapter IV. Boundary value problems. Other types of equations 263
§1. General differential expressions with constant coefficients 263
ip
§2. The problem of Dirichlet type for second order differential expres¬
sions with constant coefficients 279
§3 Equations of mixed type 298
Chapter V. General theory of expansions of selfadjoint operators in gener¬
alized eigenvectors 317
§1. Procedure for defining resolution of the identity 317
§2. Expansion in generalized eigenvectors 330
§3 Expansions in generalized eigenfunctions of operators on the
space L2(G) 344
§4. Eigenfunction expansions of Carleman operators 350
§5 Growth estimates of eigenfunctions at infinity 360
Chapter VI. Spectral theory for selfadjoint partial differential operators 375
§1. Differential operators in an unbounded region 375
§2. Spectral theory of selfadjoint elliptic operators 396
§3. Spectral theory of general selfadjoint differential operators 442
§4. Separation of variables 462
§5. Spectral theory of ordinary selfadjoint differential operators 493
Chapter VII. Spectral theory of selfadjoint difference operators 501
§1. Second order difference operators on the semi axis (Jacobi
matrices) 501
§2. Second order difference expressions with operator coefficients on
the semi axis 547
§3 Second order difference operators on the whole axis 580
§4. Partial difference operators of the second order in a half plane 588
ix
Chapter VIII. Representation of a positive definite kernel in terms of
elementary kernels 609
§1. General outline 610
§2. Existence of selfadjoint commuting extensions, and the question
of uniqueness 622
§3. Continuous positive definite kernels, * commuting with one dif¬
ferential operator 641
§4. The case of q 1 differential operators 693
§5. Positive definite kernels * commuting with difference operators 712
§6. Results connected with partial differential operators 739
Notes on the Literature 749
Introduction 749
Chapter I 749
Chapter II 751
Chapter III 751
Chapter IV 756
Chapter V 757
Chapter VI 760
Chapter VII 763
Chapter VIII 764
Bibliography 769
Subject Index 801
Notation Index 807
|
| any_adam_object | 1 |
| author | Berezanskij, Jurij M. |
| author_facet | Berezanskij, Jurij M. |
| author_role | aut |
| author_sort | Berezanskij, Jurij M. |
| author_variant | j m b jm jmb |
| building | Verbundindex |
| bvnumber | BV002969715 |
| classification_rvk | SK 500 SK 620 |
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| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T15:51:35Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001859325 |
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| physical | IX, 809 S. |
| publishDate | 1968 |
| publishDateSearch | 1968 |
| publishDateSort | 1968 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Berezanskij, Jurij M. Verfasser aut Razloženie po sobstvennym funkcijam samosoprjažennych operatorov Expansions in eigenfunctions of selfadjoint operators by Ju. M. Berezanskiĭ Providence, RI American Math. Soc. 1968 IX, 809 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 17 Aus dem Russ. übers. Spektraltheorie - Selbstadjungierter Operator Selbstadjungierter Operator (DE-588)4180810-1 gnd rswk-swf Eigenfunktionenentwicklung (DE-588)4151168-2 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Eigenfunktion (DE-588)4151167-0 gnd rswk-swf Operator (DE-588)4130529-2 gnd rswk-swf Differentialgleichung (DE-588)4012249-9 s Spektraltheorie (DE-588)4116561-5 s DE-604 Eigenfunktion (DE-588)4151167-0 s Selbstadjungierter Operator (DE-588)4180810-1 s Operator (DE-588)4130529-2 s Eigenfunktionenentwicklung (DE-588)4151168-2 s 1\p DE-604 Translations of mathematical monographs 17 (DE-604)BV000002394 17 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001859325&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Berezanskij, Jurij M. Expansions in eigenfunctions of selfadjoint operators Translations of mathematical monographs Spektraltheorie - Selbstadjungierter Operator Selbstadjungierter Operator (DE-588)4180810-1 gnd Eigenfunktionenentwicklung (DE-588)4151168-2 gnd Differentialgleichung (DE-588)4012249-9 gnd Spektraltheorie (DE-588)4116561-5 gnd Eigenfunktion (DE-588)4151167-0 gnd Operator (DE-588)4130529-2 gnd |
| subject_GND | (DE-588)4180810-1 (DE-588)4151168-2 (DE-588)4012249-9 (DE-588)4116561-5 (DE-588)4151167-0 (DE-588)4130529-2 |
| title | Expansions in eigenfunctions of selfadjoint operators |
| title_alt | Razloženie po sobstvennym funkcijam samosoprjažennych operatorov |
| title_auth | Expansions in eigenfunctions of selfadjoint operators |
| title_exact_search | Expansions in eigenfunctions of selfadjoint operators |
| title_full | Expansions in eigenfunctions of selfadjoint operators by Ju. M. Berezanskiĭ |
| title_fullStr | Expansions in eigenfunctions of selfadjoint operators by Ju. M. Berezanskiĭ |
| title_full_unstemmed | Expansions in eigenfunctions of selfadjoint operators by Ju. M. Berezanskiĭ |
| title_short | Expansions in eigenfunctions of selfadjoint operators |
| title_sort | expansions in eigenfunctions of selfadjoint operators |
| topic | Spektraltheorie - Selbstadjungierter Operator Selbstadjungierter Operator (DE-588)4180810-1 gnd Eigenfunktionenentwicklung (DE-588)4151168-2 gnd Differentialgleichung (DE-588)4012249-9 gnd Spektraltheorie (DE-588)4116561-5 gnd Eigenfunktion (DE-588)4151167-0 gnd Operator (DE-588)4130529-2 gnd |
| topic_facet | Spektraltheorie - Selbstadjungierter Operator Selbstadjungierter Operator Eigenfunktionenentwicklung Differentialgleichung Spektraltheorie Eigenfunktion Operator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001859325&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
| work_keys_str_mv | AT berezanskijjurijm razlozenieposobstvennymfunkcijamsamosoprjazennychoperatorov AT berezanskijjurijm expansionsineigenfunctionsofselfadjointoperators |