The Mellin transformation and Fuchsian type partial differential equations:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer Acad. Publ.
1992
|
| Series: | Mathematics and its applications / East European series
56 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 223 S. |
| ISBN: | 0792316835 |
Staff View
MARC
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| 245 | 1 | 0 | |a The Mellin transformation and Fuchsian type partial differential equations |c by Zofia Szmydt and Bogdan Ziemian |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer Acad. Publ. |c 1992 | |
| 300 | |a XIV, 223 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Mathematics and its applications / East European series |v 56 | |
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| 650 | 4 | |a Differential equations, Partial | |
| 650 | 4 | |a Mellin transform | |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
Series Editor s Preface vii
Preface xiii
Chapter I. Introduction
§1. Terminology and notation 1
§2. Elementary facts on complex topological vector spaces 5
1. Multinormed complex vector spaces and their duals 5
2. Inductive and projective limits 7
3. Subspaces. The Hahn Banach theorem 8
Exercise 9
§3. A review of basic facts in the theory of distributions 9
1. Spaces DK and (DK) 9
2. Spaces D(A) and D (A) 9
3. Spaces S and S 15
4. Spaces E and E 16
5. Substitution in distributions. Homogeneous distributions 16
6. Classical order of a distribution and extendibility theorems for
distributions 17
7. Convolution of distributions 19
8. Tensor product of distributions 20
Exercises 21
Chapter II. Mellin distributions and the Mellin transformation
§4. The Fourier and the Fourier Mellin transformations 27
1. The Fourier transformation in S 27
2. The Fourier Mellin transformation in the space of Mellin
distributions with support in R+ 30
Exercises 32
§5. The spaces of Mellin distributions with support in a polyinterval 34
1. Spaces Ma ((0,t]) and M a ((0,*]) 34
2. Spaces M(w) ((0,t]) and M[u) ((0,t]) 41
Exercises 46
§6. Operations of multiplication and differentiation in the space
of Mellin distributions 48
ix
x Contents
1. Multiplication and differentiation in Ma, M(w) and their duals ... 48
2. Mellin multipliers 49
Exercises 52
§7. The Mellin transformation in the space of Mellin distributions 54
1. The Mellin transformation in the space of Mellin distributions
and its relations with the Fourier Laplace transformation 55
2. Examples of Mellin transforms of some functions 60
3. Mellin transforms of certain cut off functions 67
3.1. One dimensional smooth cut off functions 67
3.2. n Dimensional smooth cut off functions with a parameter .... 71
Exercises 73
§8. The structure of Mellin distributions 76
1. Characterizations of Mellin distributions 76
2. Substitution in a Mellin distribution 82
3. Mellin order of a Mellin distribution 86
Exercises 87
§9. Paley Wiener type theorems for the Mellin transformation 87
Exercises 98
§10. Mellin transforms of cut off functions (continued) 100
1. Conical cut off functions 100
2. The if inequalities 105
3. The tangent cones Ek and related cut off functions 106
4* Further investigation of the Mellin transform of a conical cut off
function Ill
Exercises 114
§11. Important subspaces of Mellin distributions 115
1. Subspaces M( »} 115
2. Subspaces SPr(s, s ) of Mellin distributions 119
3. Spaces M(Q; g) and Zd(Q; q) of distributions with continuous
radial asymptotics 121
Exercises 124
§12. The modified Cauchy transformation 125
1. Modified Cauchy and Hilbert transformations in dimension 1 ... 125
2. The case with parameters 128
Exercises 137
Contents xi
Chapter III. Fuchsian type singular operators
§13. Fuchsian type ordinary differential operators 139
1. Asymptotic expansions 139
2. The equation P(xj^)u = f and definition of ordinary Fuchsian
type differential operators 144
3. Case of smooth coefficients 146
4. Case of analytic coefficients 152
5. Special functions as generalized analytic functions 162
Exercises 174
§14. Elliptic Fuchsian type partial differential equations in spaces M! .. 175
1. Existence and regularity of solutions on tangent cones Ek 176
2. Case of a proper cone 185
Exercise 187
§15. Fuchsian type partial differential equations in spaces with continuous
radial asymptotics 188
1. The radial characteristic set Char,j P 190
2. Regularity of solutions in spaces M(/2; g) and Z {Q g) 196
Appendix. Generalized smooth functions and theory of resurgent
functions of Jean Ecalle 205
1. Introduction 205
2. Generalized Taylor expansions 206
3. Algebra of resurgent functions of Jean Ecalle 208
4. Applications 209
Bibliography 215
List of Symbols 219
Subject Index 221
|
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| discipline | Mathematik |
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| id | DE-604.BV005920158 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:36:53Z |
| institution | BVB |
| isbn | 0792316835 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003707170 |
| oclc_num | 25409092 |
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| physical | XIV, 223 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series2 | Mathematics and its applications / East European series |
| spelling | Szmydt, Zofia 1923-2010 Verfasser (DE-588)1292642696 aut The Mellin transformation and Fuchsian type partial differential equations by Zofia Szmydt and Bogdan Ziemian Dordrecht u.a. Kluwer Acad. Publ. 1992 XIV, 223 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications / East European series 56 Equations aux dérivées partielles ram Mellin, transformation de ram Differential equations, Partial Mellin transform Fuchs-Differentialgleichung (DE-588)4155564-8 gnd rswk-swf Mellin-Transformation (DE-588)4339148-5 gnd rswk-swf Mellin-Transformation (DE-588)4339148-5 s Fuchs-Differentialgleichung (DE-588)4155564-8 s DE-604 Ziemian, Bogdan Verfasser aut East European series Mathematics and its applications 56 (DE-604)BV000006709 56 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003707170&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Szmydt, Zofia 1923-2010 Ziemian, Bogdan The Mellin transformation and Fuchsian type partial differential equations Equations aux dérivées partielles ram Mellin, transformation de ram Differential equations, Partial Mellin transform Fuchs-Differentialgleichung (DE-588)4155564-8 gnd Mellin-Transformation (DE-588)4339148-5 gnd |
| subject_GND | (DE-588)4155564-8 (DE-588)4339148-5 |
| title | The Mellin transformation and Fuchsian type partial differential equations |
| title_auth | The Mellin transformation and Fuchsian type partial differential equations |
| title_exact_search | The Mellin transformation and Fuchsian type partial differential equations |
| title_full | The Mellin transformation and Fuchsian type partial differential equations by Zofia Szmydt and Bogdan Ziemian |
| title_fullStr | The Mellin transformation and Fuchsian type partial differential equations by Zofia Szmydt and Bogdan Ziemian |
| title_full_unstemmed | The Mellin transformation and Fuchsian type partial differential equations by Zofia Szmydt and Bogdan Ziemian |
| title_short | The Mellin transformation and Fuchsian type partial differential equations |
| title_sort | the mellin transformation and fuchsian type partial differential equations |
| topic | Equations aux dérivées partielles ram Mellin, transformation de ram Differential equations, Partial Mellin transform Fuchs-Differentialgleichung (DE-588)4155564-8 gnd Mellin-Transformation (DE-588)4339148-5 gnd |
| topic_facet | Equations aux dérivées partielles Mellin, transformation de Differential equations, Partial Mellin transform Fuchs-Differentialgleichung Mellin-Transformation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003707170&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000006709 |
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