Spectral properties of noncommuting operators:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2004
|
| Series: | Lecture Notes in Mathematics
1843 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 184 S. |
| ISBN: | 3540219234 |
Staff View
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| 245 | 1 | 0 | |a Spectral properties of noncommuting operators |c Brian Jefferies |
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Introduction 1
2 Weyl Calculus 13
2.1 Background 13
2.2 Operators of Paley Wiener Type s 16
2.3 The Joint Spectrum 21
3 Clifford Analysis 27
3.1 Clifford Algebras 27
3.2 Banach Modules 29
3.3 Cauchy Formula 30
3.4 Vector Valued Functions 32
3.5 Monogenic Expansions 33
3.6 Monogenic Representation of Distributions 35
3.7 Plane Wave Decomposition 35
3.8 Approximation 36
4 Functional Calculus for Noncommuting Operators 39
4.1 The Weyl Calculus and the Cauchy Kernel 39
4.2 The Joint Spectrum and the Cauchy Kernel 44
4.3 The Monogenic Functional Calculus 52
4.4 Spectral Decomposition 60
5 The Joint Spectrum of Matrices 67
5.1 Nelson s Formula for Hermitian Matrices 67
5.2 Exponential Bounds for Matrices 73
5.2.1 Perturbation 74
5.2.2 The Exponential Bound 77
5.3 The Joint Spectrum of Pairs of Hermitian Matrices 80
5.3.1 The Numerical Range of Matrices 81
5.3.2 Examples 88
5.3.3 The Joint Spectrum of Two Hermitian Matrices 88
VIII Contents
5.4 Simultaneously Triangularisable Matrices 104
5.4.1 Disintegration of Measures 106
5.4.2 The Image of Simplicial Measure 107
5.4.3 Joint Spectrum of Triangularisable Matrices 110
5.5 Systems of Matrices Ill
6 The Monogenic Calculus for Sectorial Operators 123
6.1 The #°° Functional Calculus for a Single Operator 124
6.2 The Cauchy Kernel for n Sectorial Operators 126
6.3 Monogenic and Holomorphic Functions in Sectors 130
6.3.1 Joint Spectral Theory in the Algebra C(n) 130
6.3.2 Plane Wave Decompositions 135
6.3.3 Bounded Monogenic Functions in a Sector 137
6.4 Bounded Holomorphic Functions in Sectors 140
6.4.1 Sectors in Cn 140
6.4.2 Fourier Analysis in Sectors 142
6.5 The Monogenic Calculus for n Sectorial Operators 153
7 Feynman s Operational Calculus 157
7.1 Operants for the Weyl Calculus 157
7.2 Feynman s // Operational Calculus for n Operators 160
7.3 The /tt Monogenic Calculus for n Operators 165
References 173
Index of Notation 181
Index 183
|
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| indexdate | 2024-07-09T19:58:19Z |
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| isbn | 3540219234 |
| language | English |
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| physical | VIII, 184 S. |
| publishDate | 2004 |
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| series | Lecture Notes in Mathematics |
| series2 | Lecture Notes in Mathematics |
| spelling | Jefferies, Brian Verfasser aut Spectral properties of noncommuting operators Brian Jefferies Berlin [u.a.] Springer 2004 VIII, 184 S. txt rdacontent n rdamedia nc rdacarrier Lecture Notes in Mathematics 1843 Nicht vertauschbarer Operator - Spektraltheorie Functional analysis Linear operators Operator theory Nicht vertauschbarer Operator (DE-588)4303614-4 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Nicht vertauschbarer Operator (DE-588)4303614-4 s Spektraltheorie (DE-588)4116561-5 s DE-604 Lecture Notes in Mathematics 1843 (DE-604)BV000676446 1843 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012817146&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jefferies, Brian Spectral properties of noncommuting operators Lecture Notes in Mathematics Nicht vertauschbarer Operator - Spektraltheorie Functional analysis Linear operators Operator theory Nicht vertauschbarer Operator (DE-588)4303614-4 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| subject_GND | (DE-588)4303614-4 (DE-588)4116561-5 |
| title | Spectral properties of noncommuting operators |
| title_auth | Spectral properties of noncommuting operators |
| title_exact_search | Spectral properties of noncommuting operators |
| title_full | Spectral properties of noncommuting operators Brian Jefferies |
| title_fullStr | Spectral properties of noncommuting operators Brian Jefferies |
| title_full_unstemmed | Spectral properties of noncommuting operators Brian Jefferies |
| title_short | Spectral properties of noncommuting operators |
| title_sort | spectral properties of noncommuting operators |
| topic | Nicht vertauschbarer Operator - Spektraltheorie Functional analysis Linear operators Operator theory Nicht vertauschbarer Operator (DE-588)4303614-4 gnd Spektraltheorie (DE-588)4116561-5 gnd |
| topic_facet | Nicht vertauschbarer Operator - Spektraltheorie Functional analysis Linear operators Operator theory Nicht vertauschbarer Operator Spektraltheorie |
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