Distributions, integral transforms, and applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Taylor & Francis
2003
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Analytical methods and special functions
7 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | VI, 148 S. |
| ISBN: | 041526958X |
Internformat
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Datensatz im Suchindex
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| adam_text | DISTRIBUTIONS, INTEGRAL TRANSFORMS AND APPLICATIONS WLADYSLAW KIERAT AND
URSZULA SZTABA TAYLOR & FRANCIS TAYLOR & FRANCIS CROUP LONDON AND NEW
YORK CONTENTS PREFACE VII CHAPTER 1. DEFINITIONS AND PRELIMINARIES 1
1.1. THE SPACES V AND 1 1.2. APPROXIMATION LEMMAS 3 1.3.
REGULARIZATIONS OF FUNCTIONS 5 1.4. DU BOIS-RYMOND S LEMMA 6 1.5. SOME
DENSITY THEOREM 7 1.6. DISTRIBUTIONAL CONVERGENCE 8 1.7. ALGEBRAIC
OPERATIONS ON DISTRIBUTIONS 9 1.8. LINEAR TRANSFORMATIONS IN THE SPACE
OF THE INDEPENDENT VARIABLES 10 1.9. DIFFERENTIATION OF DISTRIBUTIONS 11
1.10. WEAK DERIVATIVES OF LOCALLY INTEGRABLE FUNCTIONS 12 1.11. LOCAL
SOBOLEV SPACES 16 1.12. SOBOLEV SPACES 19 1.13. DIFFERENTIAL EQUATIONS
OF THE SECOND ORDER WITH MEASURES AS COEFFICIENTS 21 CHAPTER 2. LOCAL
PROPERTIES OF DISTRIBUTIONS 27 2.1. SMOOTH PARTITIONS OF UNITY 27 2.2.
APPROXIMATION OF FUNCTIONS BELONGING TO W M P (FI) BY SMOOTH FUNCTIONS
29 2.3. RESTRICTIONS OF DISTRIBUTIONS 31 2.4. SUPPORT OF DISTRIBUTIONS
33 2.5. DISTRIBUTIONS OF FINITE ORDER 35 2.6. CARTESIAN PRODUCTS OF
BANACH SPACES 37 2.7. SOME LOCAL REPRESENTATIONS OF DISTRIBUTIONS 38
CHAPTER 3. TENSOR PRODUCTS AND CONVOLUTION PRODUCTS 41 3.1.
REGULARIZATION OF DISTRIBUTIONS 41 3.2. A CHARACTERIZATION OF
CONVOLUTION OPERATORS 44 3.3. TENSOR PRODUCT OF DISTRIBUTIONS * 45 3.4.
DIFFERENTIATION AND SUPPORT OF TENSOR PRODUCT 47 3.5. THE THEOREM OF
KERNELS 48 3.6. CONNECTION BETWEEN TENSOR PRODUCT AND CONVOLUTION
PRODUCT OF DISTRIBUTIONS 54 3.7. DIFFERENTIATION AND SUPPORT OF
CONVOLUTION PRODUCT 58 CHAPTER 4. DIFFERENTIAL EQUATIONS 59 4.1.
FUNDAMENTAL SOLUTIONS OF DIFFERENTIAL EQUATIONS 59 VI CONTENTS 4.2. THE
CAUCHY PROBLEM FOR THE WAVE EQUATION WITH DISTRIBUTION DATA 60 4.3.
FUNDAMENTAL SOLUTIONS OF THE LAPLACE OPERATOR AND THE HEAT OPERATOR 63
4.4. THE HORMANDER INEQUALITIES 66 4.5. L 2 -SOLVABILITY 70 4.6.
REGULARITY PROPERTIES OF DIFFERENTIAL OPERATORS 72 CHAPTER 5. PARTICULAR
TYPES OF DISTRIBUTIONS AND CAUCHY TRANSFORMS 75 5.1. INTEGRABLE
DISTRIBUTIONS 75 5.2. REGULARIZATION OF INTEGRABLE DISTRIBUTIONS 77 5.3.
TENSOR PRODUCT OF INTEGRABLE DISTRIBUTIONS 78 5.4. V LP AND V LP SPACES
81 5.5. CONVOLUTION PRODUCT 82 5.6. CAUCHY TRANSFORMS OF INTEGRABLE
DISTRIBUTIONS 84 5.7. CAUCHY TRANSFORMS OF DISTRIBUTIONS BELONGING TO
T LP 87 5.8. CAUCHY TRANSFORMS OF SOME DISTRIBUTIONS 91 CHAPTER 6.
TEMPERED DISTRIBUTIONS AND FOURIER TRANSFORMS 95 6.1. THE SPACES S AND
6.2. TENSOR PRODUCT OF TEMPERED DISTRIBUTIONS 97 6.3. FOURIER TRANSFORMS
OF INTEGRABLE FUNCTIONS 98 6.4. FORMAL PROPERTIES OF FOURIER TRANSFORMS
100 6.5. FOURIER TRANSFORMS OF FUNCTIONS IN IS 102 6.6. FOURIER
TRANSFORMS OF FUNCTIONS IN L 2 (K ) 103 6.7. FOURIER TRANSFORMS OF THE
HERMITE FUNCTIONS 107 6.8. FOURIER TRANSFORMS OF TEMPERED DISTRIBUTIONS
108 6.9. FORMAL PROPERTIES OF FOURIER TRANSFORMS OF TEMPERED
DISTRIBUTIONS 109 6.10. FOURIER TRANSFORMS OF INTEGRABLE DISTRIBUTIONS
110 6.11. FOURIER TRANSFORMS OF SQUARE INTEGRABLE DISTRIBUTIONS 112
6.12. DETERMINING FOURIER TRANSFORMS OF SQUARE INTEGRABLE DISTRIBUTIONS
114 6.13. HILBERT TRANSFORMS 116 6.14. CARLEMAN TRANSFORMS 117 6.15. THE
PALEYA-WIENER TYPE THEOREMS 119 6.16. THE CAUCHY SEMIGROUP 121 6.17. THE
CAUCHY PROBLEM FOR THE HEAT EQUATION 123 CHAPTER 7. ORTHOGONAL
EXPANSIONS OF DISTRIBUTIONS 127 7.1. THE POISSON SUMMATION FORMULA 127
7.2. PERIODIC DISTRIBUTIONS 128 7.3. THE SPACES A AND A 131 7.4. CAUCHY
TRANSFORMS OF ELEMENTS OF A 134 7.5. THE WIENER EXPANSION OF SQUARE
INTEGRABLE DISTRIBUTIONS 136 APPENDIX. SEQUENTIAL COMPLETENESS OF SOME
SPACES 139 SUBJECT INDEX 143 NOTES AND REFERENCES TO THE LITERATURE 145
BIBLIOGRAPHY 147 INDEX OF SYMBOLS 149
|
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| id | DE-604.BV014807761 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:07:24Z |
| institution | BVB |
| isbn | 041526958X |
| language | English |
| lccn | 2002075069 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010019707 |
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| physical | VI, 148 S. |
| publishDate | 2003 |
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| publisher | Taylor & Francis |
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| series | Analytical methods and special functions |
| series2 | Analytical methods and special functions |
| spelling | Kierat, Wladyslaw Verfasser aut Distributions, integral transforms, and applications Wladyslaw Kierat and Urszula Sztaba 1. publ. London [u.a.] Taylor & Francis 2003 VI, 148 S. txt rdacontent n rdamedia nc rdacarrier Analytical methods and special functions 7 Includes bibliographical references and index Integral transforms Theory of distributions (Functional analysis) Integraltransformation (DE-588)4027235-7 gnd rswk-swf Distribution Funktionalanalysis (DE-588)4070505-5 gnd rswk-swf Distribution Funktionalanalysis (DE-588)4070505-5 s Integraltransformation (DE-588)4027235-7 s DE-604 Sztaba, Urszula Sonstige oth Analytical methods and special functions 7 (DE-604)BV011932737 7 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010019707&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kierat, Wladyslaw Distributions, integral transforms, and applications Analytical methods and special functions Integral transforms Theory of distributions (Functional analysis) Integraltransformation (DE-588)4027235-7 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd |
| subject_GND | (DE-588)4027235-7 (DE-588)4070505-5 |
| title | Distributions, integral transforms, and applications |
| title_auth | Distributions, integral transforms, and applications |
| title_exact_search | Distributions, integral transforms, and applications |
| title_full | Distributions, integral transforms, and applications Wladyslaw Kierat and Urszula Sztaba |
| title_fullStr | Distributions, integral transforms, and applications Wladyslaw Kierat and Urszula Sztaba |
| title_full_unstemmed | Distributions, integral transforms, and applications Wladyslaw Kierat and Urszula Sztaba |
| title_short | Distributions, integral transforms, and applications |
| title_sort | distributions integral transforms and applications |
| topic | Integral transforms Theory of distributions (Functional analysis) Integraltransformation (DE-588)4027235-7 gnd Distribution Funktionalanalysis (DE-588)4070505-5 gnd |
| topic_facet | Integral transforms Theory of distributions (Functional analysis) Integraltransformation Distribution Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010019707&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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