Theory and applications of convolution integral equations:
Gespeichert in:
| Vorheriger Titel: | Srivastava, Hari M. Convolution integral equations with special function kernels |
|---|---|
| Hauptverfasser: | , |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
1992
|
| Schriftenreihe: | Mathematics and its applications
79 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XX, 240 S. |
| ISBN: | 0792318919 |
Internformat
MARC
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| 100 | 1 | |a Srivastava, Hari M. |d 1940- |e Verfasser |0 (DE-588)12358874X |4 aut | |
| 245 | 1 | 0 | |a Theory and applications of convolution integral equations |c by H. M. Srivastava and R. G. Buschman |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1992 | |
| 300 | |a XX, 240 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 79 | |
| 650 | 7 | |a Convolutions (Mathématiques) |2 ram | |
| 650 | 7 | |a Noyaux (Mathématiques) |2 ram | |
| 650 | 7 | |a Volterra, équations de - Solutions numériques |2 ram | |
| 650 | 4 | |a Convolutions (Mathematics) | |
| 650 | 4 | |a Kernel functions | |
| 650 | 4 | |a Volterra equations |x Numerical solutions | |
| 650 | 0 | 7 | |a Faltung |g Mathematik |0 (DE-588)4141470-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Faltungsintegral |0 (DE-588)4142843-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Integralgleichung |0 (DE-588)4027229-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Faltungsintegral |0 (DE-588)4142843-2 |D s |
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| 689 | 1 | 0 | |a Faltung |g Mathematik |0 (DE-588)4141470-6 |D s |
| 689 | 1 | 1 | |a Integralgleichung |0 (DE-588)4027229-1 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Buschman, Robert G. |e Verfasser |4 aut | |
| 780 | 0 | 0 | |i Frühere Aufl. u.d.T. |a Srivastava, Hari M. |t Convolution integral equations with special function kernels |
| 830 | 0 | |a Mathematics and its applications |v 79 |w (DE-604)BV008163334 |9 79 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003624251&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-003624251 | ||
Datensatz im Suchindex
| _version_ | 1804119983811198976 |
|---|---|
| adam_text | TABLE OF CONTENTS
PREFACE xi
ACKNOWLEDGEMENTS xiv
INTRODUCTION xv
CHAPTER 1. PRELIMINARIES ON SPECIAL FUNCTION KERNELS
1.1. Algebraic kernels 1
1.2. Exponential, logarithmic, and trigonometric kernels 2
1.3. Chebyshev polynomials 3
1.4. Legendre polynomials and functions 4
1.5. Gegenbauer and Jacobi polynomials 5
1.6. Laguerre and Hermite polynomials 6
1.7. Bessel functions 7
1.8. Rummer s and Whittaker s functions 8
1.9. Gauss hypergeometric function 9
1.10. Generalized hypergeometric and other functions 10
1.11. Further integral equations with multivariable kernels 13
CHAPTER 2. BASIC PROPERTIES AND THEOREMS
2.1. Convolutions and relations among equations 15
2.2. The Theorem of Titchmarsh and the uniqueness of solutions 19
2.3. Associated integral transformations 20
2.4. Associated fractional integrals 21
2.5. Simple kernel variations 24
CHAPTER 3. METHODS AND ILLUSTRATIVE EXAMPLES
3.1. Rodrigues formula 26
3.2. Resolvent kernel 27
3.3. Laplace transformation 29
3.4. Mellin and other transformations 42
3.5. Fractional integrals 45
3.6. Mikusiriski operators 48
3.7. Other methods 53
viii Table of Contents
CHAPTER 4. MISCELLANEOUS RESULTS AND OPEN QUESTIONS
4.1. Some immediate consequences from tables of integral transforms 56
4.2. Simplifications of generalized hypergeometric kernels 59
4.3. Confluent hypergeometric functions of several variables 64
4.4. Some open questions 68
CHAPTER 5. EQUATIONS OF THE SECOND AND OTHER KINDS
5.1. General properties of equations of the second kind 70
5.2. Algebraic kernels 72
5.3. Exponential, trigonometric, and hyperbolic kernels 73
5.4. Higher transcendental functions 75
5.5. Integro differential equations 76
5.6. Equations of the third kind 77
5.7. Non linear equations 79
CHAPTER 6. CONVOLUTIONS OVER OTHER INTERVALS
6.1. Convolutions over (x, oc) 81
6.2. Equations on the interval (x, oc) 84
6.3. Equations on the interval (0, oo) 86
6.4. Equations on the interval ( —oo, +oo) 100
6.5. Equations on the interval [a, b] 101
APPENDIX. LIST OF SYMBOLS 104
INVERSION TABLES. INDEX 114
TABLE 1. / k(x t)f(t)dt = g{x) 116
Jo
TABLE 2. g(x) + f k(x t)f(t)dt = f(x) 158
Jo
TABLE 3. / k(t x)f(t)(U = j(x) 167
J 1
TABLE 4. / k(r/t)f(1)dt = g(.v) 172
Jo
/¦oc /.oo
TABLE 5. The forms / k(.vt)f(t)dt and / t~lk(x/t)f(t)dt 180
Jo Jo
TABLE 6. The form / k(x t)f(t)dt 187
Jo
y + OO
TABLE 7. The form / k(x t)f(t)dt 189
i oo
TABLE 8. The form / k(x t)f(t)dt 192
Table of Contents ix
BIBLIOGRAPHY 195
AUTHOR INDEX 230
SUBJECT INDEX 234
|
| any_adam_object | 1 |
| author | Srivastava, Hari M. 1940- Buschman, Robert G. |
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| author_role | aut aut |
| author_sort | Srivastava, Hari M. 1940- |
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| bvnumber | BV005798994 |
| callnumber-first | Q - Science |
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| classification_rvk | SK 640 |
| classification_tum | MAT 465f MAT 452f |
| ctrlnum | (OCoLC)26096199 (DE-599)BVBBV005798994 |
| dewey-full | 515/.45 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.45 |
| dewey-search | 515/.45 |
| dewey-sort | 3515 245 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV005798994 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:34:52Z |
| institution | BVB |
| isbn | 0792318919 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003624251 |
| oclc_num | 26096199 |
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| owner_facet | DE-12 DE-739 DE-91 DE-BY-TUM DE-703 DE-522 DE-83 DE-11 DE-188 |
| physical | XX, 240 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Srivastava, Hari M. 1940- Verfasser (DE-588)12358874X aut Theory and applications of convolution integral equations by H. M. Srivastava and R. G. Buschman Dordrecht [u.a.] Kluwer 1992 XX, 240 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 79 Convolutions (Mathématiques) ram Noyaux (Mathématiques) ram Volterra, équations de - Solutions numériques ram Convolutions (Mathematics) Kernel functions Volterra equations Numerical solutions Faltung Mathematik (DE-588)4141470-6 gnd rswk-swf Faltungsintegral (DE-588)4142843-2 gnd rswk-swf Integralgleichung (DE-588)4027229-1 gnd rswk-swf Faltungsintegral (DE-588)4142843-2 s DE-604 Faltung Mathematik (DE-588)4141470-6 s Integralgleichung (DE-588)4027229-1 s Buschman, Robert G. Verfasser aut Frühere Aufl. u.d.T. Srivastava, Hari M. Convolution integral equations with special function kernels Mathematics and its applications 79 (DE-604)BV008163334 79 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003624251&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Srivastava, Hari M. 1940- Buschman, Robert G. Theory and applications of convolution integral equations Mathematics and its applications Convolutions (Mathématiques) ram Noyaux (Mathématiques) ram Volterra, équations de - Solutions numériques ram Convolutions (Mathematics) Kernel functions Volterra equations Numerical solutions Faltung Mathematik (DE-588)4141470-6 gnd Faltungsintegral (DE-588)4142843-2 gnd Integralgleichung (DE-588)4027229-1 gnd |
| subject_GND | (DE-588)4141470-6 (DE-588)4142843-2 (DE-588)4027229-1 |
| title | Theory and applications of convolution integral equations |
| title_auth | Theory and applications of convolution integral equations |
| title_exact_search | Theory and applications of convolution integral equations |
| title_full | Theory and applications of convolution integral equations by H. M. Srivastava and R. G. Buschman |
| title_fullStr | Theory and applications of convolution integral equations by H. M. Srivastava and R. G. Buschman |
| title_full_unstemmed | Theory and applications of convolution integral equations by H. M. Srivastava and R. G. Buschman |
| title_old | Srivastava, Hari M. Convolution integral equations with special function kernels |
| title_short | Theory and applications of convolution integral equations |
| title_sort | theory and applications of convolution integral equations |
| topic | Convolutions (Mathématiques) ram Noyaux (Mathématiques) ram Volterra, équations de - Solutions numériques ram Convolutions (Mathematics) Kernel functions Volterra equations Numerical solutions Faltung Mathematik (DE-588)4141470-6 gnd Faltungsintegral (DE-588)4142843-2 gnd Integralgleichung (DE-588)4027229-1 gnd |
| topic_facet | Convolutions (Mathématiques) Noyaux (Mathématiques) Volterra, équations de - Solutions numériques Convolutions (Mathematics) Kernel functions Volterra equations Numerical solutions Faltung Mathematik Faltungsintegral Integralgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003624251&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
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