Introduction to Hilbert space and the theory of spectral multiplicity:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
AMS Chelsea Publ.
1998
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| Ausgabe: | 2. ed., [Nachdr.] |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 114 S. |
| ISBN: | 0821813781 |
Internformat
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| 245 | 1 | 0 | |a Introduction to Hilbert space and the theory of spectral multiplicity |c Paul R. Halmos |
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Datensatz im Suchindex
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| adam_text | INTRODUCTION TO HILBERT SPACE AND THE THEORY OF SPECTRAL MULTIPLICITY
PAUL R. HALMOS SECOND EDITION AMS CHELSEA PUBLISHING AMERICAN
MATHEMATICAL SOCIETY * PROVIDENCE, RHODE ISLAND CONTENTS PAGE PREFACE 3
§0. PREREQUISITES AND NOTATION 8 CHAPTER I THE GEOMETRY OF HILBERT SPACE
§1. LINEAR FUNCTIONALS 11 §2. BILINEAR FUNCTIONALS 12 §3. QUADRATIC
FORMS 12 §4. INNER PRODUCT AND NORM 13 §5. THE INEQUALITIES OF BESSEL
AND SCHWARZ 14 §6. HUBERT SPACE 16 §7. INFINITE SUMS 17 §8. CONDITIONS
FOR SUMMABILITY 19 §9. EXAMPLES OF HUBERT SPACES 20 §10. SUBSPACES 21
§11. VECTORS IN AND OUT OF SUBSPACES 23 §12. ORTHOGONAL COMPLEMENTS 24
§13. VECTOR SUMS 25 §14. BASES 27 §15. A NON-CLOSED VECTOR SUM 28 §16.
DIMENSION 29 §17. BOUNDEDNESS 31 §18. BOUNDED BILINEAR FUNCTIONALS 32
CHAPTER II THE ALGEBRA OF OPERATORS §19. OPERATORS 35 §20. EXAMPLES OF
OPERATORS 36 §21. INVERSES 37 §22. ADJOINTS 38 §23. INVARIANCE 40 5 6
CONTENTS §24. HERMITIAN OPERATORS 41 §25. NORMAL AND UNITARY OPERATORS
42 §26. PROJECTIONS 43 §27. PROJECTIONS AND SUBSPACES 44 §28. SUMS OF
PROJECTIONS 46 §29. PRODUCTS AND DIFFERENCES OF PROJECTIONS 47 §30.
INFIMA AND SUPREMA OF PROJECTIONS 49 §31. THE SPECTRUM OF AN OPERATOR 50
§32. COMPACTNESS OF SPECTRA 52 §33. TRANSFORMS OF SPECTRA 53 §34. THE
SPECTRUM OF A HERMITIAN OPERATOR 54 §35. SPECTRAL HEURISTICS 56 §36.
SPECTRAL MEASURES 58 §37. SPECTRAL INTEGRALS 60 §38. REGULAER SPECTRAL
MEASURES 61 §39. REAL AND COMPLEX SPECTRAL MEASURES 63 §40. COMPLEX
SPECTRAL INTEGRALS 65 §41. DESCRIPTION OF THE SPECTRAL SUBSPACES 66 §42.
CHARACTERIZATION OF THE SPECTRAL SUBSPACES 68 §43. THE SPECTRAL THEOREM
FOR HERMITIAN OPERATORS 69 §44. THE SPECTRAL THEOREM FOR NORMAL
OPERATORS 71 CHAPTER III THE ANALYSIS OF SPECTRAL MEASURES §45. THE
PROBLEM OF UNITARY EQUIVALENCE 74 §46. MULTIPLICITY FUNCTIONS IN
FINITE-DIMENSIONAL SPACES 76 §47. MEASURES 77 §48. BOOLEAN OPERATIONS ON
MEASURES 79 §49. MULTIPLICITY FUNCTIONS 80 §50. THE CANONICAL EXAMPLE OF
A SPECTRAL MEASURE 83 §51. FINITE-DIMENSIONAL SPECTRAL MEASURES 84 §52.
SIMPLE FINITE-DIMENSIONAL SPECTRAL MEASURES 85 §53. THE COMMUTATOR OF A
SET OF PROJECTIONS 87 §54. PAIRS OF COMMUTATORS 88 §55. COLUMNS 89 §56.
ROWS 90 §57. CYCLES 91 §58. SEPARABLE PROJECTIONS 92 §59.
CHARACTERIZATIONS OF ROWS 93 CONTENTS 7 §60. CYCLES AND ROWS 95 §61. THE
EXISTENCE OF ROWS 96 §62. ORTHOGONAL SYSTEMS 97 §63. THE POWER OF A
MAXIMAL ORTHOGONAL SYSTEM 99 §64. MULTIPLICITIES 100 §65. MEASURES FROM
VECTORS 102 §66. SUBSPACES FROM MEASURES 104 §67. THE MULTIPLICITY
FUNCTION OF A SPECTRAL MEASURE 106 §68. CONCLUSION 108 REFERENCES 109
BLBLIOORAPHY 112 S
|
| any_adam_object | 1 |
| author | Halmos, Paul R. 1916-2006 |
| author_GND | (DE-588)118746677 |
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| author_sort | Halmos, Paul R. 1916-2006 |
| author_variant | p r h pr prh |
| building | Verbundindex |
| bvnumber | BV012679315 |
| classification_rvk | SK 600 |
| classification_tum | MAT 463f |
| ctrlnum | (OCoLC)245745609 (DE-599)BVBBV012679315 |
| discipline | Mathematik |
| edition | 2. ed., [Nachdr.] |
| format | Book |
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| id | DE-604.BV012679315 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:31:48Z |
| institution | BVB |
| isbn | 0821813781 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008617713 |
| oclc_num | 245745609 |
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| owner_facet | DE-91 DE-BY-TUM DE-355 DE-BY-UBR |
| physical | 114 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | AMS Chelsea Publ. |
| record_format | marc |
| spelling | Halmos, Paul R. 1916-2006 Verfasser (DE-588)118746677 aut Introduction to Hilbert space and the theory of spectral multiplicity Paul R. Halmos 2. ed., [Nachdr.] New York [u.a.] AMS Chelsea Publ. 1998 114 S. txt rdacontent n rdamedia nc rdacarrier Hilbert-Raum Mehrparametrige Spektraltheorie Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Spektralmaß (DE-588)4182167-1 gnd rswk-swf Operator (DE-588)4130529-2 gnd rswk-swf Operatortheorie (DE-588)4075665-8 gnd rswk-swf Spektralmaß (DE-588)4182167-1 s DE-604 Operator (DE-588)4130529-2 s Spektraltheorie (DE-588)4116561-5 s Hilbert-Raum (DE-588)4159850-7 s Operatortheorie (DE-588)4075665-8 s 1\p DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008617713&sequence=000001&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 | Halmos, Paul R. 1916-2006 Introduction to Hilbert space and the theory of spectral multiplicity Hilbert-Raum Mehrparametrige Spektraltheorie Hilbert-Raum (DE-588)4159850-7 gnd Spektraltheorie (DE-588)4116561-5 gnd Spektralmaß (DE-588)4182167-1 gnd Operator (DE-588)4130529-2 gnd Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4159850-7 (DE-588)4116561-5 (DE-588)4182167-1 (DE-588)4130529-2 (DE-588)4075665-8 |
| title | Introduction to Hilbert space and the theory of spectral multiplicity |
| title_auth | Introduction to Hilbert space and the theory of spectral multiplicity |
| title_exact_search | Introduction to Hilbert space and the theory of spectral multiplicity |
| title_full | Introduction to Hilbert space and the theory of spectral multiplicity Paul R. Halmos |
| title_fullStr | Introduction to Hilbert space and the theory of spectral multiplicity Paul R. Halmos |
| title_full_unstemmed | Introduction to Hilbert space and the theory of spectral multiplicity Paul R. Halmos |
| title_short | Introduction to Hilbert space and the theory of spectral multiplicity |
| title_sort | introduction to hilbert space and the theory of spectral multiplicity |
| topic | Hilbert-Raum Mehrparametrige Spektraltheorie Hilbert-Raum (DE-588)4159850-7 gnd Spektraltheorie (DE-588)4116561-5 gnd Spektralmaß (DE-588)4182167-1 gnd Operator (DE-588)4130529-2 gnd Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Hilbert-Raum Mehrparametrige Spektraltheorie Spektraltheorie Spektralmaß Operator Operatortheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008617713&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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