Introduction to the spectral theory of polynomial operator pencils:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Providence
American Mathemat. Soc.
1988
|
| Series: | Translations of mathematical monographs
71 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Russ. übers. |
| Physical Description: | IV, 250 S. |
| ISBN: | 0821845233 |
Staff View
MARC
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| 240 | 1 | 0 | |a Vvedenie v spektral'nuju teoriju polinomial'nych operatornych pučkov |
| 245 | 1 | 0 | |a Introduction to the spectral theory of polynomial operator pencils |c A. S. Markus |
| 264 | 1 | |a Providence |b American Mathemat. Soc. |c 1988 | |
| 300 | |a IV, 250 S. | ||
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| 650 | 4 | |a Spectre (Mathématiques) | |
| 650 | 7 | |a Théorie spectrale (Mathématiques) |2 ram | |
| 650 | 4 | |a Polynomial operator pencils | |
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Record in the Search Index
| _version_ | 1804116867083665408 |
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| adam_text | Table of Contents
INTRODUCTION 1
CHAPTER I. OPERATORS WITH COMPACT RESOLVENT
WHICH ARE CLOSE TO BEING NORMAL 7
§ 1. Auxiliary propositions from function theory 7
§2. Main definitions and known results 11
§3. Relatively compact perturbations and a lemma of Keldysh 14
§4. The theorem of Keldysh on completeness of the root vectors 18
§5. Lemmas on /7 subordinate perturbations 20
§6. Convergence of expansions in root vectors 25
§7. The perturbation determinant 38
§8. The behavior of the spectrum under a relatively compact
perturbation 40
§9. The behavior of the spectrum under a ^ subordinate
perturbation 47
§10. Elliptic differential operators close to being selfadjoint 52
CHAPTER II. KELDYSH PENCILS 55
§11. Holomorphic operator valued functions 55
§12. Polynomial pencils and their linearization 58
§ 13. Derived chains and multiple completeness 63
§ 14. A second method of linearization 69
§ 15. Multiple completeness and spectral asymptotics for a
Keldysh pencil 74
§16. Convergence of multiple expansions 80
§ 17. Left Keldysh pencils 83
§ 18. A direct proof of the Keldysh theorem on multiple
completeness 89
§19. A theorem on completeness with finite defect for one
spectral series of a Keldysh pencil 96
§20. Pencils with unbounded coefficients 102
iii
iv TABLE OF CONTENTS
§21. Some applications 108
CHAPTER III. FACTORIZATION OF PENCILS 111
§22. Divisors of a pencil and canonical factorization 111
§23. A theorem on factorization of an element in a Banach
algebra which is close to the identity, and applications of it 120
§24. Factorization of an accretive operator valued function on the
circle 125
§25. Factorization of an accretive operator valued function
having one simple pole inside a contour 130
§26. The roots of the quadratic form of a pencil and the spectral
divisors of a pencil 137
§27. Factorization of matrix pencils and a characteristic property
of circles 146
§28. Operator roots of a pencil and invariant subspaces of the
linearizer 151
§29. The Vandermonde operator 156
CHAPTER IV. SELFADJOINT PENCILS 163
§30. Spectral roots similar to selfadjoint operators, and Riesz
bases of eigenvectors of a pencil 163
§31. Hyperbolic pencils 169
§32. Variational methods in the investigation of the eigenvalues
and eigenvectors of a continuous operator valued function 185
§33. A Riesz basis of eigenvectors of a holomorphic
operator valued function, in a subspace with finite defect 191
§34. Factorization of nonnegative operator valued functions and
elliptic pencils 197
§35. An application of operator theory in a space with an
indefinite metric 206
APPENDIX. M. V. Keldysh, On the eigenvalues and eigenfunctions
of certain classes of nonselfadjoint equations 215
BRIEF COMMENTS ON THE LITERATURE 221
BIBLIOGRAPHY 229
SUBJECT INDEX 247
LIST OF NOTATION 249
|
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| dewey-sort | 3515.7 3246 |
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| id | DE-604.BV002447691 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:45:19Z |
| institution | BVB |
| isbn | 0821845233 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001585423 |
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| physical | IV, 250 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | American Mathemat. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs |
| spelling | Markus, Aleksandr S. Verfasser aut Vvedenie v spektral'nuju teoriju polinomial'nych operatornych pučkov Introduction to the spectral theory of polynomial operator pencils A. S. Markus Providence American Mathemat. Soc. 1988 IV, 250 S. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 71 Aus d. Russ. übers. Faisceaux d'opérateurs polynomiaux Spectre (Mathématiques) Théorie spectrale (Mathématiques) ram Polynomial operator pencils Spectral theory (Mathematics) Polynomoperator (DE-588)4175267-3 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Operatorbüschel (DE-588)4231492-6 gnd rswk-swf Polynomoperator (DE-588)4175267-3 s Operatorbüschel (DE-588)4231492-6 s Spektraltheorie (DE-588)4116561-5 s DE-604 Translations of mathematical monographs 71 (DE-604)BV000002394 71 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001585423&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Markus, Aleksandr S. Introduction to the spectral theory of polynomial operator pencils Translations of mathematical monographs Faisceaux d'opérateurs polynomiaux Spectre (Mathématiques) Théorie spectrale (Mathématiques) ram Polynomial operator pencils Spectral theory (Mathematics) Polynomoperator (DE-588)4175267-3 gnd Spektraltheorie (DE-588)4116561-5 gnd Operatorbüschel (DE-588)4231492-6 gnd |
| subject_GND | (DE-588)4175267-3 (DE-588)4116561-5 (DE-588)4231492-6 |
| title | Introduction to the spectral theory of polynomial operator pencils |
| title_alt | Vvedenie v spektral'nuju teoriju polinomial'nych operatornych pučkov |
| title_auth | Introduction to the spectral theory of polynomial operator pencils |
| title_exact_search | Introduction to the spectral theory of polynomial operator pencils |
| title_full | Introduction to the spectral theory of polynomial operator pencils A. S. Markus |
| title_fullStr | Introduction to the spectral theory of polynomial operator pencils A. S. Markus |
| title_full_unstemmed | Introduction to the spectral theory of polynomial operator pencils A. S. Markus |
| title_short | Introduction to the spectral theory of polynomial operator pencils |
| title_sort | introduction to the spectral theory of polynomial operator pencils |
| topic | Faisceaux d'opérateurs polynomiaux Spectre (Mathématiques) Théorie spectrale (Mathématiques) ram Polynomial operator pencils Spectral theory (Mathematics) Polynomoperator (DE-588)4175267-3 gnd Spektraltheorie (DE-588)4116561-5 gnd Operatorbüschel (DE-588)4231492-6 gnd |
| topic_facet | Faisceaux d'opérateurs polynomiaux Spectre (Mathématiques) Théorie spectrale (Mathématiques) Polynomial operator pencils Spectral theory (Mathematics) Polynomoperator Spektraltheorie Operatorbüschel |
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