Computability in analysis and physics:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1989
|
| Series: | Perspectives in mathematical logic
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 206 S. graph. Darst. |
| ISBN: | 3540500359 0387500359 |
Staff View
MARC
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| 245 | 1 | 0 | |a Computability in analysis and physics |c Marian B. Pour-El ; J. Ian Richards |
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Record in the Search Index
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| adam_text | Contents
Introduction 1
Prerequisites from Logic and Analysis 6
Part I. Computability in Classical Analysis 9
Chapter 0. An Introduction to Computable Analysis 11
Introduction 11
1. Computable Real Numbers 13
2. Computable Sequences of Real Numbers 17
3. Computable Functions of One or Several Real Variables 24
4. Preliminary Constructs in Analysis 28
5. Basic Constructs of Analysis 33
6. The Max Min Theorem and the Intermediate Value Theorem ... 40
7. Proof of the Effective Weierstrass Theorem 44
Chapter 1. Further Topics in Computable Analysis 50
Introduction 50
1. C Functions, 1 n oo 51
2. Analytic Functions 59
3. The Effective Modulus Lemma and Some of Its Consequences ... 64
4. Translation Invariant Operators 69
Part II. The Computability Theory of Banach Spaces 75
Chapter 2. Computability Structures on a Banach Space 77
Introduction 77
1. The Axioms for a Computability Structure 80
2. The Classical Case: Computability in the Sense of Chapter 0 .... 82
3. Intrinsic Lp computability 83
X Contents
4. Intrinsic /p computability 85
5. The Effective Density Lemma and the Stability Lemma 85
6. Two Counterexamples: Separability Versus Effective Separability
and Computability on L°°[0, 1] 88
7. Ad Hoc Computability Structures 90
Chapter 3. The First Main Theorem and Its Applications 93
Introduction 93
1. Bounded Operators, Closed Unbounded Operators 96
2. The First Main Theorem 101
3. Simple Applications to Real Analysis 104
4. Further Applications to Real Analysis 108
5. Applications to Physical Theory 115
Part III. The Computability Theory of Eigenvalues and Eigenvectors ... 121
Chapter 4. The Second Main Theorem, the Eigenvector Theorem, and
Related Results 123
Introduction 123
1. Basic Notions for Unbounded Operators, Effectively Determined
Operators 125
2. The Second Main Theorem and Some of Its Corollaries 128
3. Creation and Destruction of Eigenvalues 130
4. A Non normal Operator with a Noncomputable Eigenvalue .... 132
5. The Eigenvector Theorem 133
6. The Eigenvector Theorem, Completed 139
7. Some Results for Banach Spaces 142
Chapter 5. Proof of the Second Main Theorem 149
Introduction 149
1. Review of the Spectral Theorem 151
2. Preliminaries 158
3. Heuristics 166
4. The Algorithm 175
5. Proof That the Algorithm Works 177
6. Normal Operators 184
7. Unbounded Self Adjoint Operators 187
8. Converses 188
Addendum: Open Problems 192
Bibliography 195
Subject Index 201
|
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| id | DE-604.BV002436147 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:45:13Z |
| institution | BVB |
| isbn | 3540500359 0387500359 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001581152 |
| oclc_num | 243397593 |
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| physical | X, 206 S. graph. Darst. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | Springer |
| record_format | marc |
| series2 | Perspectives in mathematical logic |
| spelling | Pour-El, Marian B. Verfasser aut Computability in analysis and physics Marian B. Pour-El ; J. Ian Richards Berlin [u.a.] Springer 1989 X, 206 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Perspectives in mathematical logic Berechenbare Funktion (DE-588)4135762-0 gnd rswk-swf Berechenbarkeit (DE-588)4138368-0 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Analysis (DE-588)4001865-9 s Berechenbarkeit (DE-588)4138368-0 s DE-604 Berechenbare Funktion (DE-588)4135762-0 s Mathematische Physik (DE-588)4037952-8 s Richards, J. Ian Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001581152&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pour-El, Marian B. Richards, J. Ian Computability in analysis and physics Berechenbare Funktion (DE-588)4135762-0 gnd Berechenbarkeit (DE-588)4138368-0 gnd Analysis (DE-588)4001865-9 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4135762-0 (DE-588)4138368-0 (DE-588)4001865-9 (DE-588)4037952-8 |
| title | Computability in analysis and physics |
| title_auth | Computability in analysis and physics |
| title_exact_search | Computability in analysis and physics |
| title_full | Computability in analysis and physics Marian B. Pour-El ; J. Ian Richards |
| title_fullStr | Computability in analysis and physics Marian B. Pour-El ; J. Ian Richards |
| title_full_unstemmed | Computability in analysis and physics Marian B. Pour-El ; J. Ian Richards |
| title_short | Computability in analysis and physics |
| title_sort | computability in analysis and physics |
| topic | Berechenbare Funktion (DE-588)4135762-0 gnd Berechenbarkeit (DE-588)4138368-0 gnd Analysis (DE-588)4001865-9 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Berechenbare Funktion Berechenbarkeit Analysis Mathematische Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001581152&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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