Complex analysis and special topics in harmonic analysis:
A companion volume to the text Complex Variables: An Introduction by the same authors, this book further develops the theory of holomorphic functions, continuing to emphasize the role that the Cauchy-Riemann equation plays in modern complex analysis. Topics considered include boundary values of holo...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY ; Berlin ; Heidelberg
Springer
1995
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | A companion volume to the text Complex Variables: An Introduction by the same authors, this book further develops the theory of holomorphic functions, continuing to emphasize the role that the Cauchy-Riemann equation plays in modern complex analysis. Topics considered include boundary values of holomorphic functions in the sense of distributions and hyperfunctions; L[superscript 2]-estimates for solutions of the Cauchy-Riemann equation, interpolation problems, and ideal theory in algebras of entire functions with growth conditions; exponential polynomials; the G transform and the unifying role it plays in complex analysis and transcendental number theory; summation methods; and the spectral synthesis theorem of L. Schwartz concerning the solutions of a homogeneous convolution equation on the real line and its applications in harmonic analysis By providing an overview of current research and open problems, as well as topics that have wide applications in engineering, this book should be of interest to mathematicians and applied mathematicians, as well as to graduate students beginning their research |
| Beschreibung: | X, 482 Seiten graph. Darst. |
| ISBN: | 0387944117 |
Internformat
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| 520 | 3 | |a A companion volume to the text Complex Variables: An Introduction by the same authors, this book further develops the theory of holomorphic functions, continuing to emphasize the role that the Cauchy-Riemann equation plays in modern complex analysis. Topics considered include boundary values of holomorphic functions in the sense of distributions and hyperfunctions; L[superscript 2]-estimates for solutions of the Cauchy-Riemann equation, interpolation problems, and ideal theory in algebras of entire functions with growth conditions; exponential polynomials; the G transform and the unifying role it plays in complex analysis and transcendental number theory; summation methods; and the spectral synthesis theorem of L. Schwartz concerning the solutions of a homogeneous convolution equation on the real line and its applications in harmonic analysis | |
| 520 | |a By providing an overview of current research and open problems, as well as topics that have wide applications in engineering, this book should be of interest to mathematicians and applied mathematicians, as well as to graduate students beginning their research | ||
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| 650 | 7 | |a Functies (wiskunde) |2 gtt | |
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| 650 | 7 | |a analyse harmonique |2 inriac | |
| 650 | 7 | |a fonction holomorphe |2 inriac | |
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| 689 | 1 | 0 | |a Harmonische Analyse |0 (DE-588)4023453-8 |D s |
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Datensatz im Suchindex
| _version_ | 1804124829538844672 |
|---|---|
| adam_text | Contents
Preface vii
CHAPTER 1
Boundary Values of Holomorphic Functions and
Analytic Functionals 1
1.1. The Hardy Spaces in the Disk 2
1.2. Hyperfunctions 35
1.3. Analytic Functionals and Entire Functions of Exponential Type 51
1.4. Vade Mecum of Functional Analysis 77
1.5. Convolution of Analytic Functionals 85
1.6. Analytic Functionals on the Unit Circle 94
CHAPTER 2
Interpolation and the Algebras Ap 109
2.1. The Algebras A 109
2.2. Interpolation with Growth Conditions 118
2.3. Ideal Theory in Ap 136
2.4. Dense Ideals in Ap(Q) 160
2.5. Local Ideals and Conductor Ideals in Ap 166
2.6. The Algebra Ap of Entire Functions of Order at Most p 170
CHAPTER 3
Exponential Polynomials 198
3.1. The Ring of Exponential Polynomials 198
3.2. Distributions of Zeros of an Exponential Polynomial 217
CHAPTER 4
Integral Valued Entire Functions 260
4.1. The G Transform 260
4.2. Integral Valued Entire Functions 278
ix
x Contents
CHAPTER 5
Summation Methods 299
5.1. Borel and Mittag Leffler Summation Methods 299
5.2. The Lindelof Indicator Function 316
5.3. The Fourier Borel Transform of Order p of Analytic Functionals 326
5.4. Analytic Functionals with Noncompact Carrier 333
CHAPTER 6
Harmonic Analysis 353
6.1. Convolution Equations in U 354
6.2. Convolution Equations in C 385
6.3. The Equation f(z + 1) /(z) = g(z) 405
6.4. Differential Operators of Infinite Order 419
6.5. Deconvolution 458
References 471
Notation 479
Index 481
|
| any_adam_object | 1 |
| author | Berenstein, Carlos A. 1944-2019 Gay, Roger |
| author_GND | (DE-588)130607010 |
| author_facet | Berenstein, Carlos A. 1944-2019 Gay, Roger |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.9 |
| dewey-search | 515/.9 |
| dewey-sort | 3515 19 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV010403069 |
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| indexdate | 2024-07-09T17:51:53Z |
| institution | BVB |
| isbn | 0387944117 |
| language | English |
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| physical | X, 482 Seiten graph. Darst. |
| publishDate | 1995 |
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| spelling | Berenstein, Carlos A. 1944-2019 Verfasser (DE-588)130607010 aut Complex analysis and special topics in harmonic analysis Carlos A. Berenstein, Roger Gay New York, NY ; Berlin ; Heidelberg Springer 1995 X, 482 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier A companion volume to the text Complex Variables: An Introduction by the same authors, this book further develops the theory of holomorphic functions, continuing to emphasize the role that the Cauchy-Riemann equation plays in modern complex analysis. Topics considered include boundary values of holomorphic functions in the sense of distributions and hyperfunctions; L[superscript 2]-estimates for solutions of the Cauchy-Riemann equation, interpolation problems, and ideal theory in algebras of entire functions with growth conditions; exponential polynomials; the G transform and the unifying role it plays in complex analysis and transcendental number theory; summation methods; and the spectral synthesis theorem of L. Schwartz concerning the solutions of a homogeneous convolution equation on the real line and its applications in harmonic analysis By providing an overview of current research and open problems, as well as topics that have wide applications in engineering, this book should be of interest to mathematicians and applied mathematicians, as well as to graduate students beginning their research Analyse harmonique ram Complexe variabelen gtt Fonctions d'une variable complexe ram Fourier-analyse gtt Functies (wiskunde) gtt analyse complexe inriac analyse harmonique inriac fonction holomorphe inriac théorie fonction inriac Functions of complex variables Harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 gnd rswk-swf Funktionentheorie (DE-588)4018935-1 s DE-604 Harmonische Analyse (DE-588)4023453-8 s Gay, Roger Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006926859&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Berenstein, Carlos A. 1944-2019 Gay, Roger Complex analysis and special topics in harmonic analysis Analyse harmonique ram Complexe variabelen gtt Fonctions d'une variable complexe ram Fourier-analyse gtt Functies (wiskunde) gtt analyse complexe inriac analyse harmonique inriac fonction holomorphe inriac théorie fonction inriac Functions of complex variables Harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| subject_GND | (DE-588)4023453-8 (DE-588)4018935-1 |
| title | Complex analysis and special topics in harmonic analysis |
| title_auth | Complex analysis and special topics in harmonic analysis |
| title_exact_search | Complex analysis and special topics in harmonic analysis |
| title_full | Complex analysis and special topics in harmonic analysis Carlos A. Berenstein, Roger Gay |
| title_fullStr | Complex analysis and special topics in harmonic analysis Carlos A. Berenstein, Roger Gay |
| title_full_unstemmed | Complex analysis and special topics in harmonic analysis Carlos A. Berenstein, Roger Gay |
| title_short | Complex analysis and special topics in harmonic analysis |
| title_sort | complex analysis and special topics in harmonic analysis |
| topic | Analyse harmonique ram Complexe variabelen gtt Fonctions d'une variable complexe ram Fourier-analyse gtt Functies (wiskunde) gtt analyse complexe inriac analyse harmonique inriac fonction holomorphe inriac théorie fonction inriac Functions of complex variables Harmonic analysis Harmonische Analyse (DE-588)4023453-8 gnd Funktionentheorie (DE-588)4018935-1 gnd |
| topic_facet | Analyse harmonique Complexe variabelen Fonctions d'une variable complexe Fourier-analyse Functies (wiskunde) analyse complexe analyse harmonique fonction holomorphe théorie fonction Functions of complex variables Harmonic analysis Harmonische Analyse Funktionentheorie |
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