Linear transformations in Hilbert space and their applications to analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Soc.
1970
|
| Edition: | 7. print. |
| Series: | American Mathematical Society: Colloquium publications
15 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 622 S. |
| ISBN: | 0821810154 |
Staff View
MARC
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| 245 | 1 | 0 | |a Linear transformations in Hilbert space and their applications to analysis |c by Marshall Harvey Stone |
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| 264 | 1 | |a Providence, RI |b American Mathematical Soc. |c 1970 | |
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Record in the Search Index
| _version_ | 1804121296835969024 |
|---|---|
| adam_text | CONTENTS
CHAPTER I
ABSTRACT HILBERT SPACE AND ITS REALIZATIONS
§ 1. The Concept of Space 1
§ 2. Abstract Hilbert Space 2
§ 3. Abstract Unitary Spaces 16
§ 4. Linear Manifolds in Hilbert Space 18
§ 5. Eealizations of Abstract Hilbert Space 23
CHAPTER II
TRANSFORMATIONS IN HILBERT SPACE
§ 1. Linear Transformations 33
§ 2. Symmetric Transformations 49
§ 3. Bounded Linear Transformations 53
§ 4. Projections 70
§ 5. Isometric and Unitary Transformations 76
§ 6. Unitary Invariance 83
CHAPTER III
EXAMPLES OF LINEAR TRANSFORMATIONS
§ 1. Infinite Matrices 86
§ 2. Integral Operators 98
§ 3. Differential Operators 112
§ 4. Operators of Other Types 124
CHAPTER IV
RESOLVENTS, SPECTRA, REDUCIBILITY
§ 1. The Fundamental Problems 125
§ 2. Resolvents and Spectra 128
§ 3. Reducibility 150
CHAPTER V
SELF ADJOINT TRANSFORMATIONS
§ 1. Analytical Methods 155
§ 2. Analytical Representation of the Resolvent 165
§ 3. The Reducibility of the Resolvent 172
vii
Viii CONTENTS
Page
§ 4. The Analytical Eepresentation of a Self Adjoint
Transformation 180
§ 5. The Spectrum of a Self Adjoint Transformation .. 184
CHAPTER VI
THE OPERATIONAL CALCULUS
§ 1. The Radon Stieltjes Integral 198
§ 2. The Operational Calculus 221
CHAPTER VII
THE UNITARY EQUIVALENCE
OP SELF ADJOINT TRANSFORMATIONS
§ 1. Preparatory Theorems 242
§ 2. Unitary Equivalence 247
§ 3. Self Adjoint Transformations with Simple Spectra 275
§ 4. The Reducibility of Self Adjoint Transformations . 288
§ 5. Reduction to Principal Axes 294
CHAPTER VIII
GENERAL TYPES OF LINEAR TRANSFORMATIONS
§ 1. Permutability 299
§ 2. Unitary Transformations 302
§ 3. Normal Transformations 311
§ 4. A Theorem on Factorization.. 331
CHAPTER IX
SYMMETRIC TRANSFORMATIONS
§ 1. The General Theory 334
§ 2. Real Transformations , 357
§ 3. Approximation Theorems 365
CHAPTER X
APPLICATIONS
§ 1. Integral Operators 397
§ 2. Ordinary Differential Operators of the First Order 424
§ 3. Ordinary Differential Operators of the Second Order 448
§ 4. Jacobi Matrices and Allied Topics 530
Index 615
|
| any_adam_object | 1 |
| author | Stone, Marshall H. 1903-1989 |
| author_GND | (DE-588)118799037 |
| author_facet | Stone, Marshall H. 1903-1989 |
| author_role | aut |
| author_sort | Stone, Marshall H. 1903-1989 |
| author_variant | m h s mh mhs |
| building | Verbundindex |
| bvnumber | BV007109588 |
| classification_rvk | SK 620 |
| ctrlnum | (OCoLC)630485099 (DE-599)BVBBV007109588 |
| discipline | Mathematik |
| edition | 7. print. |
| format | Book |
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| id | DE-604.BV007109588 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:55:44Z |
| institution | BVB |
| isbn | 0821810154 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004527113 |
| oclc_num | 630485099 |
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| owner | DE-355 DE-BY-UBR DE-29T |
| owner_facet | DE-355 DE-BY-UBR DE-29T |
| physical | VIII, 622 S. |
| publishDate | 1970 |
| publishDateSearch | 1970 |
| publishDateSort | 1970 |
| publisher | American Mathematical Soc. |
| record_format | marc |
| series | American Mathematical Society: Colloquium publications |
| series2 | American Mathematical Society: Colloquium publications |
| spelling | Stone, Marshall H. 1903-1989 Verfasser (DE-588)118799037 aut Linear transformations in Hilbert space and their applications to analysis by Marshall Harvey Stone 7. print. Providence, RI American Mathematical Soc. 1970 VIII, 622 S. txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: Colloquium publications 15 Hilbert, Espacio de Transformaciones (Matematicas) Lineare Transformation (DE-588)4167712-2 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Linearer Operator (DE-588)4167721-3 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 s Lineare Transformation (DE-588)4167712-2 s DE-604 Funktionalanalysis (DE-588)4018916-8 s Linearer Operator (DE-588)4167721-3 s 1\p DE-604 American Mathematical Society: Colloquium publications 15 (DE-604)BV035417609 15 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004527113&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 | Stone, Marshall H. 1903-1989 Linear transformations in Hilbert space and their applications to analysis American Mathematical Society: Colloquium publications Hilbert, Espacio de Transformaciones (Matematicas) Lineare Transformation (DE-588)4167712-2 gnd Funktionalanalysis (DE-588)4018916-8 gnd Linearer Operator (DE-588)4167721-3 gnd Hilbert-Raum (DE-588)4159850-7 gnd |
| subject_GND | (DE-588)4167712-2 (DE-588)4018916-8 (DE-588)4167721-3 (DE-588)4159850-7 |
| title | Linear transformations in Hilbert space and their applications to analysis |
| title_auth | Linear transformations in Hilbert space and their applications to analysis |
| title_exact_search | Linear transformations in Hilbert space and their applications to analysis |
| title_full | Linear transformations in Hilbert space and their applications to analysis by Marshall Harvey Stone |
| title_fullStr | Linear transformations in Hilbert space and their applications to analysis by Marshall Harvey Stone |
| title_full_unstemmed | Linear transformations in Hilbert space and their applications to analysis by Marshall Harvey Stone |
| title_short | Linear transformations in Hilbert space and their applications to analysis |
| title_sort | linear transformations in hilbert space and their applications to analysis |
| topic | Hilbert, Espacio de Transformaciones (Matematicas) Lineare Transformation (DE-588)4167712-2 gnd Funktionalanalysis (DE-588)4018916-8 gnd Linearer Operator (DE-588)4167721-3 gnd Hilbert-Raum (DE-588)4159850-7 gnd |
| topic_facet | Hilbert, Espacio de Transformaciones (Matematicas) Lineare Transformation Funktionalanalysis Linearer Operator Hilbert-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004527113&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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