Classical function theory, operator dilation theory, and machine computation on multiply-connected domains:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2008
|
| Series: | Memoirs of the American Mathematical Society
892 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 191, number 892 (second of 5 numbers)." Includes bibliographical references |
| Physical Description: | VII, 159 S. graph. Darst. |
| ISBN: | 9780821840467 |
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| 245 | 1 | 0 | |a Classical function theory, operator dilation theory, and machine computation on multiply-connected domains |c Jim Agler ; John Harland ; Benjamin J. Raphael |
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Record in the Search Index
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| adam_text | MEMOIRS 1VA OF THE AMERICAN MATHEMATICAL SOCIETY NUMBER 892 CLASSICAL
FUNCTION THEORY, OPERATOR DILATION THEORY, AND MACHINE COMPUTATION ON
MULTIPLY-CONNECTED DOMAINS JIM AGLER JOHN HARLAND BENJAMIN J. RAPHAEL
JANUARY 2008 * VOLUME 191 * NUMBER 892 (SECOND OF 5 NUMBERS) * ISSN
0065-9266 AMERICAN MATHEMATICAL SOCIETY PROVIDENCE, RHODE ISLAND
CONTENTS PREFACE VII CHAPTER 1. GENERALIZATIONS OF THE HERGLOTZ
REPRESENTATION THEOREM, VON NEUMANN S INEQUALITY AND THE SZ.-NAGY
DILATION THEOREM TO MULTIPLY CONNECTED DOMAINS 1 1.1. INTRODUCTION 1
1.2. PRELIMINARIES , 7 1.3. THE FIRST HERGLOTZ REPRESENTATION 12 1.4.
THE SECOND HERGLOTZ REPRESENTATION 21 1.5. THE THIRD HERGLOTZ
REPRESENTATION 23 1.6. THE HERGLOTZ REPRESENTATIONS AND OPERATOR THEORY
28 1.7. AN APPLICATION 33 CHAPTER 2. THE COMPUTATIONAL GENERATION OF
COUNTEREXAMPLES TO THE RATIONAL DILATION CONJECTURE 61 2.1. INTRODUCTION
61 2.2. MATHEMATICAL PRELIMINARIES 64 2.3. ANALYSIS OF THE DILATION
CONDITION FOR NONSINGULARLY HYPEREXTREMAL GRAMMIANS 72 2.4. ANALYSIS OF
DILATION EXTREMAL GRAMMIANS 82 2.5. ALGORITHMS 89 2.6. A COMPUTATIONAL
COUNTEREXAMPLE 100 2.7. PLAUSIBILITY ARGUMENTS 105 CHAPTER 3. ARBITRARY
PRECISION COMPUTATIONS OF THE POISSON KERNEL AND HERGLOTZ KERNELS ON
MULTIPLY-CONNECTED CIRCLE DOMAINS 109 3.1. INTRODUCTION 109 3.2.
COMPUTATION OF THE FUNCTIONS 112 3.3. RESULTS 119 CHAPTER 4. SCHWARTZ
KERNELS ON MULTIPLY CONNECTED DOMAINS 127 APPENDIX A. CONVERGENCE
RESULTS 139 APPENDIX B. EXAMPLE INNER PRODUCT COMPUTATION 155
BIBLIOGRAPHY 157
|
| adam_txt |
"MEMOIRS 1VA OF THE AMERICAN MATHEMATICAL SOCIETY NUMBER 892 CLASSICAL
FUNCTION THEORY, OPERATOR DILATION THEORY, AND MACHINE COMPUTATION ON
MULTIPLY-CONNECTED DOMAINS JIM AGLER JOHN HARLAND BENJAMIN J. RAPHAEL
JANUARY 2008 * VOLUME 191 * NUMBER 892 (SECOND OF 5 NUMBERS) * ISSN
0065-9266 AMERICAN MATHEMATICAL SOCIETY PROVIDENCE, RHODE ISLAND
CONTENTS PREFACE VII CHAPTER 1. GENERALIZATIONS OF THE HERGLOTZ
REPRESENTATION THEOREM, VON NEUMANN'S INEQUALITY AND THE SZ.-NAGY
DILATION THEOREM TO MULTIPLY CONNECTED DOMAINS 1 1.1. INTRODUCTION 1
1.2. PRELIMINARIES , 7 1.3. THE FIRST HERGLOTZ REPRESENTATION 12 1.4.
THE SECOND HERGLOTZ REPRESENTATION 21 1.5. THE THIRD HERGLOTZ
REPRESENTATION 23 1.6. THE HERGLOTZ REPRESENTATIONS AND OPERATOR THEORY
28 1.7. AN APPLICATION 33 CHAPTER 2. THE COMPUTATIONAL GENERATION OF
COUNTEREXAMPLES TO THE RATIONAL DILATION CONJECTURE 61 2.1. INTRODUCTION
61 2.2. MATHEMATICAL PRELIMINARIES 64 2.3. ANALYSIS OF THE DILATION
CONDITION FOR NONSINGULARLY HYPEREXTREMAL GRAMMIANS 72 2.4. ANALYSIS OF
DILATION EXTREMAL GRAMMIANS 82 2.5. ALGORITHMS 89 2.6. A COMPUTATIONAL
COUNTEREXAMPLE 100 2.7. PLAUSIBILITY ARGUMENTS 105 CHAPTER 3. ARBITRARY
PRECISION COMPUTATIONS OF THE POISSON KERNEL AND HERGLOTZ KERNELS ON
MULTIPLY-CONNECTED CIRCLE DOMAINS 109 3.1. INTRODUCTION 109 3.2.
COMPUTATION OF THE FUNCTIONS 112 3.3. RESULTS 119 CHAPTER 4. SCHWARTZ
KERNELS ON MULTIPLY CONNECTED DOMAINS 127 APPENDIX A. CONVERGENCE
RESULTS 139 APPENDIX B. EXAMPLE INNER PRODUCT COMPUTATION 155
BIBLIOGRAPHY 157 |
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| discipline | Mathematik |
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| illustrated | Illustrated |
| index_date | 2024-07-02T19:57:50Z |
| indexdate | 2024-07-09T21:12:13Z |
| institution | BVB |
| isbn | 9780821840467 |
| language | English |
| lccn | 2007060555 |
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| physical | VII, 159 S. graph. Darst. |
| publishDate | 2008 |
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| series | Memoirs of the American Mathematical Society |
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| spelling | Agler, Jim 1951- Verfasser (DE-588)1185705627 aut Classical function theory, operator dilation theory, and machine computation on multiply-connected domains Jim Agler ; John Harland ; Benjamin J. Raphael Providence, RI American Math. Soc. 2008 VII, 159 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 892 "Volume 191, number 892 (second of 5 numbers)." Includes bibliographical references Geometric function theory Operator theory Dilation theory (Operator theory) Functional analysis Analytic functions Analytische Funktion (DE-588)4142348-3 gnd rswk-swf Geometrische Funktionentheorie (DE-588)4156711-0 gnd rswk-swf Operatortheorie (DE-588)4075665-8 gnd rswk-swf Geometrische Funktionentheorie (DE-588)4156711-0 s Operatortheorie (DE-588)4075665-8 s Analytische Funktion (DE-588)4142348-3 s DE-604 Harland, John Sonstige oth Raphael, Benjamin J. Sonstige oth Memoirs of the American Mathematical Society 892 (DE-604)BV008000141 892 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016358069&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Agler, Jim 1951- Classical function theory, operator dilation theory, and machine computation on multiply-connected domains Memoirs of the American Mathematical Society Geometric function theory Operator theory Dilation theory (Operator theory) Functional analysis Analytic functions Analytische Funktion (DE-588)4142348-3 gnd Geometrische Funktionentheorie (DE-588)4156711-0 gnd Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4142348-3 (DE-588)4156711-0 (DE-588)4075665-8 |
| title | Classical function theory, operator dilation theory, and machine computation on multiply-connected domains |
| title_auth | Classical function theory, operator dilation theory, and machine computation on multiply-connected domains |
| title_exact_search | Classical function theory, operator dilation theory, and machine computation on multiply-connected domains |
| title_exact_search_txtP | Classical function theory, operator dilation theory, and machine computation on multiply-connected domains |
| title_full | Classical function theory, operator dilation theory, and machine computation on multiply-connected domains Jim Agler ; John Harland ; Benjamin J. Raphael |
| title_fullStr | Classical function theory, operator dilation theory, and machine computation on multiply-connected domains Jim Agler ; John Harland ; Benjamin J. Raphael |
| title_full_unstemmed | Classical function theory, operator dilation theory, and machine computation on multiply-connected domains Jim Agler ; John Harland ; Benjamin J. Raphael |
| title_short | Classical function theory, operator dilation theory, and machine computation on multiply-connected domains |
| title_sort | classical function theory operator dilation theory and machine computation on multiply connected domains |
| topic | Geometric function theory Operator theory Dilation theory (Operator theory) Functional analysis Analytic functions Analytische Funktion (DE-588)4142348-3 gnd Geometrische Funktionentheorie (DE-588)4156711-0 gnd Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Geometric function theory Operator theory Dilation theory (Operator theory) Functional analysis Analytic functions Analytische Funktion Geometrische Funktionentheorie Operatortheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016358069&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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