Distributions, ultradistributions and other generalized functions:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Ellis Horwood
1994
|
| Edition: | 1. publ. |
| Series: | Mathematics and its applications
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 300 S. graph. Darst. |
| ISBN: | 0132179369 |
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MARC
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Record in the Search Index
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| adam_text | Contents
Preface ix
List of Symbols xiii
1 Introduction to Distributions 1
1.1 FUNCTIONS AND GENERALISED FUNCTIONS 1
1.2 THE SCHWARTZ THEORY OF DISTRIBUTIONS 20
1.3 CALCULUS OF DISTRIBUTIONS 35
1.4 THE J.S.SILVA THEORY OF DISTRIBUTIONS 43
1.5 GENERALISED POWERS AND PSEUDO FUNCTIONS 48
2 Further Properties of Distributions 63
2.1 CONVOLUTION AND DIRECT PRODUCTS 63
2.2 CONVERGENCE OF DISTRIBUTIONS 70
2.3 SEQUENTIAL THEORIES OF DISTRIBUTIONS 80
2.4 THE MULTIPLICATION PROBLEM 85
3 Generalised Functions and Fourier Analysis 97
3.1 REVIEW OF THE CLASSICAL FOURIER TRANSFORM .... 97
3.2 GENERALISED FOURIER TRANSFORMS 108
3.3 FOURIER TRANSFORMS IN 5 113
3.4 FOURIER TRANSFORMS AND ULTRADISTRIBUTIONS .... 134
3.5 PERIODIC ULTRADISTRIBUTIONS 147
3.6 ULTRADISTRIBUTIONS OF EXPONENTIAL TYPE 150
viii Contents
4 Analytic Representation of Generalised Functions 159
4.1 THE CAUCHY TRANSFORM 159
4.2 ANALYTIC REPRESENTATION OF DISTRIBUTIONS 175
4.3 SATO HYPERFUNCTIONS ON THE LINE 184
4.4 ULTRADISTRIBUTIONS 190
4.5 THE FOURIER CARLEMAN TRANSFORM 203
5 Irregular Operations and Colombeau Generalised Functions 209
5.1 INTRINSIC PRODUCTS OF DISTRIBUTIONS 209
5.2 GENERALISED FUNCTIONS AND OPERATORS 225
5.3 CALCULUS OF GENERALISED FUNCTIONS 239
5.4 THE SCHWARTZ PRODUCT AND MULTIPLICATION IN a (HI) 249
6 Nonstandard Treatments of Generalised Functions on 1R 253
6.1 INTRODUCTION TO NONSTANDARD ANALYSIS 253
6.2 NONSTANDARD REPRESENTATIONS OF DISTRIBUTIONS . . 265
6.3 PRODUCTS OF DISTRIBUTIONS 278
6.4 THE DIFFERENTIAL ALGEBRA UQ(R) 279
6.5 CANONICAL EMBEDDING OF ECT(K.) INTO AN ALGEBRA . . 286
Bibliography 293
Index 299
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:46:08Z |
| institution | BVB |
| isbn | 0132179369 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006690040 |
| oclc_num | 30777473 |
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| physical | XIV, 300 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Ellis Horwood |
| record_format | marc |
| series2 | Mathematics and its applications |
| spelling | Hoskins, Roland F. Verfasser aut Distributions, ultradistributions and other generalized functions R. F. Hoskins and J. Sousa Pinto 1. publ. New York u.a. Ellis Horwood 1994 XIV, 300 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications Theory of distributions (Functional analysis) Distributionstheorie (DE-588)4150254-1 gnd rswk-swf Distributionstheorie (DE-588)4150254-1 s DE-188 Pinto, J. S. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006690040&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hoskins, Roland F. Pinto, J. S. Distributions, ultradistributions and other generalized functions Theory of distributions (Functional analysis) Distributionstheorie (DE-588)4150254-1 gnd |
| subject_GND | (DE-588)4150254-1 |
| title | Distributions, ultradistributions and other generalized functions |
| title_auth | Distributions, ultradistributions and other generalized functions |
| title_exact_search | Distributions, ultradistributions and other generalized functions |
| title_full | Distributions, ultradistributions and other generalized functions R. F. Hoskins and J. Sousa Pinto |
| title_fullStr | Distributions, ultradistributions and other generalized functions R. F. Hoskins and J. Sousa Pinto |
| title_full_unstemmed | Distributions, ultradistributions and other generalized functions R. F. Hoskins and J. Sousa Pinto |
| title_short | Distributions, ultradistributions and other generalized functions |
| title_sort | distributions ultradistributions and other generalized functions |
| topic | Theory of distributions (Functional analysis) Distributionstheorie (DE-588)4150254-1 gnd |
| topic_facet | Theory of distributions (Functional analysis) Distributionstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006690040&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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