A distributional approach to asymptotics: theory and applicatons
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston [u.a.]
Birkhäuser
2002
|
| Edition: | 2. ed. |
| Series: | Birkhäuser advanced texts
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 451 S. 24 cm |
| ISBN: | 0817641424 3764341424 |
Staff View
MARC
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| 245 | 1 | 0 | |a A distributional approach to asymptotics |b theory and applicatons |c Ricardo Estrada ; Ram P. Kanwal |
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Record in the Search Index
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|---|---|
| adam_text | RICARDO ESTRADA RAM P. KANWAL A DISTRIBUTIONAL APPROACH TO ASYMPTOTICS
THEORY AND APPLICATIONS SECOND EDITION BIRKHAUSER BOSTON * BASEL *
BERLIN CONTENTS PREFACE XI 1 BASIC RESULTS IN ASYMPTOTICS 1 1.1
INTRODUCTION 1 1.2 ORDER SYMBOLS 2 1.3 ASYMPTOTIC SERIES 8 1.4 ALGEBRAIC
AND ANALYTIC OPERATIONS 14 1.5 EXISTENCE OF FUNCTIONS WITH A GIVEN
ASYMPTOTIC EXPANSION . ... 18 1.6 ASYMPTOTIC POWER SERIES IN A COMPLEX
VARIABLE 21 1.7 ASYMPTOTIC APPROXIMATION OF PARTIAL SUMS 26 1.8 THE
EULER-MACLAURIN SUMMATION FORMULA 36 1.9 EXERCISES 43 2 INTRODUCTION TO
THE THEORY OF DISTRIBUTIONS 53 2.1 INTRODUCTION 53 2.2 THE SPACE OF
DISTRIBUTIONS V 55 2.3 ALGEBRAIC AND ANALYTIC OPERATIONS 59 2.4
REGULARIZATION, PSEUDOFUNCTION AND HADAMARD FINITE PART 63 2.5 SUPPORT
AND ORDER 70 2.6 HOMOGENEOUS DISTRIBUTIONS . 72 2.7 DISTRIBUTIONAL
DERIVATIVES OF DISCONTINUOUS FUNCTIONS 76 2.8 TEMPERED DISTRIBUTIONS AND
THE FOURIER TRANSFORM 82 2.9 DISTRIBUTIONS OF RAPID DECAY 87 2.10 SPACES
OF DISTRIBUTIONS ASSOCIATED WITH AN ASYMPTOTIC SEQUENCE . 90 2.11
EXERCISES 94 VIII CONTENTS 3 A DISTRIBUTIONAL THEORY FOR ASYMPTOTIC
EXPANSIONS 107 3.1 INTRODUCTION 107 3.2 THE TAYLOR EXPANSION OF
DISTRIBUTIONS 108 3.3 THE MOMENT ASYMPTOTIC EXPANSION 113 3.4 EXPANSIONS
IN THE SPACE V 121 3.5 LAPLACE S ASYMPTOTIC FORMULA 126 3.6 THE METHOD
OF STEEPEST DESCENT 132 3.7 EXPANSION OF OSCILLATORY KERNELS 142 3.8
TIME-DOMAIN ASYMPTOTICS 148 3.9 THE EXPANSION OF / (XX) AS A. -** OO IN
OTHER CASES 152 3.10 ASYMPTOTIC SEPARATION OF VARIABLES 161 3.10.1 LOCAL
BEHAVIOR 169 3.10.2 QUASI ASYMPTOTIC EXPANSIONS 170 3.11 EXERCISES 172 4
ASYMPTOTIC EXPANSION OF MULTIDIMENSIONAL GENERALIZED FUNCTIONS 187 4.1
INTRODUCTION 187 4.2 TAYLOR EXPANSION IN SEVERAL VARIABLES 188 4.3 THE
MULTIDIMENSIONAL MOMENT ASYMPTOTIC EXPANSION 191 4.4 LAPLACE S
ASYMPTOTIC FORMULA 197 4.5 FOURIER TYPE INTEGRALS 205 4.6 TIME-DOMAIN
ASYMPTOTICS 213 4.6.1 INTERIOR CRITICAL POINTS 214 4.6.2 BOUNDARY
CRITICAL POINTS 216 4.6.3 CORNERS 218 4.7 FURTHER EXAMPLES 219 4.8
TENSOR PRODUCTS AND PARTIAL ASYMPTOTIC EXPANSIONS 222 4.9 AN APPLICATION
IN QUANTUM MECHANICS 227 4.10 EXPANSION OF KERNELS OF THE TYPE/(A.X, X)
232 4.10.1 THE OPERATOR A 233 4.10.2 THE MOMENT EXPANSION OF / (A.X, X)
234 4.10.3 THE EXPANSION IN THE OTHER CASES 237 4.11 EXERCISES 242 5
ASYMPTOTIC EXPANSION OF CERTAIN SERIES CONSIDERED BY RAMANUJAN 249 5.1
INTRODUCTION 249 5.2 BASIC FORMULAS 250 5.3 LAMBERT TYPE SERIES 255 5.4
DISTRIBUTIONALLY SMALL SEQUENCES 264 5.5 MULTIPLE SERIES 273 5.6
UNRESTRICTED PARTITIONS 284 5.7 EXERCISES 292 CONTENTS CESARO BEHAVIOR
OF DISTRIBUTIONS 297 6.1 INTRODUCTION 297 6.2 SUMMABILITY OF SERIES AND
INTEGRALS 298 6.2.1 ABEL SUMMABILITY 299 6.2.2 HOLDER-CESARO-RIESZ
SUMMABILITY 301 6.3 THE BEHAVIOR OF DISTRIBUTIONS IN THE (C) SENSE 305
6.4 THE CESARO SUMMABILITY OF EVALUATIONS 308 6.5 PARAMETRIC BEHAVIOR
312 6.6 CHARACTERIZATION OF TEMPERED DISTRIBUTIONS 318 6.7 THE SPACE K!
319 6.8 SPHERICAL MEANS 323 6.9 EXISTENCE OF REGULARIZATIONS 325 6.9.1
REGULARIZATION IN SEVERAL DIMENSIONS 330 6.9.2 SINGULAR HYPERSURFACES
332 6.10 THE INTEGRAL TEST 334 6.11 MOMENT FUNCTIONS 340 6.12 THE
ANALYTIC CONTINUATION OF ZETA FUNCTIONS 346 6.13 FOURIER SERIES 352 6.14
SUMMABILITY OF TRIGONOMETRIC SERIES 357 6.15 DISTRIBUTIONAL POINT VALUES
OF FOURIER SERIES 361 6.15.1 ASYMPTOTICALLY HOMOGENEOUS FUNCTIONS 362
6.15.2 PRIMITIVES OF NULL SEQUENCES 364 6.15.3 CHARACTERIZATION OF POINT
VALUES 365 6.16 SPECTRAL ASYMPTOTICS 368 6.16.1 A SPECIAL CASE 373 6.17
POINTWISE AND AVERAGE EXPANSIONS 375 6.18 GLOBAL EXPANSIONS 382 6.19
ASYMPTOTICS OF THE COINCIDENCE LIMIT 386 6.20 EXERCISES 390 SERIES OF
DIRAC DELTA FUNCTIONS 397 7.1 INTRODUCTION 397 7.2 BASIC NOTIONS 398 7.3
SEVERAL PROBLEMS THAT LEAD TO SERIES OF DELTAS 399 7.4 DUAL TAYLOR
SERIES AS ASYMPTOTICS OF SOLUTIONS OF EQUATIONS . . . 409 7.5 BOUNDARY
LAYERS 410 7.5.1 INITIAL VALUE PROBLEMS 411 7.5.2 INNER-OUTER
DECOMPOSITION 414 7.5.3 BOUNDARY VALUE PROBLEMS 418 7.6 SPECTRAL CONTENT
ASYMPTOTICS 422 7.7 EXERCISES 430 REFERENCES 433 INDEX 447
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| author | Estrada, Ricardo 1956- Kanwal, Ram P. 1924-2006 |
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| dewey-sort | 3515 3234 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| language | English |
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| physical | XIV, 451 S. 24 cm |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Birkhäuser |
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| spelling | Estrada, Ricardo 1956- Verfasser (DE-588)121816494 aut A distributional approach to asymptotics theory and applicatons Ricardo Estrada ; Ram P. Kanwal 2. ed. Boston [u.a.] Birkhäuser 2002 XIV, 451 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Birkhäuser advanced texts Asymptotic expansions Theory of distributions (Functional analysis) Asymptotische Entwicklung (DE-588)4112609-9 gnd rswk-swf Asymptotische Entwicklung (DE-588)4112609-9 s DE-604 Kanwal, Ram P. 1924-2006 Verfasser (DE-588)1055774505 aut SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009757980&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Estrada, Ricardo 1956- Kanwal, Ram P. 1924-2006 A distributional approach to asymptotics theory and applicatons Asymptotic expansions Theory of distributions (Functional analysis) Asymptotische Entwicklung (DE-588)4112609-9 gnd |
| subject_GND | (DE-588)4112609-9 |
| title | A distributional approach to asymptotics theory and applicatons |
| title_auth | A distributional approach to asymptotics theory and applicatons |
| title_exact_search | A distributional approach to asymptotics theory and applicatons |
| title_full | A distributional approach to asymptotics theory and applicatons Ricardo Estrada ; Ram P. Kanwal |
| title_fullStr | A distributional approach to asymptotics theory and applicatons Ricardo Estrada ; Ram P. Kanwal |
| title_full_unstemmed | A distributional approach to asymptotics theory and applicatons Ricardo Estrada ; Ram P. Kanwal |
| title_short | A distributional approach to asymptotics |
| title_sort | a distributional approach to asymptotics theory and applicatons |
| title_sub | theory and applicatons |
| topic | Asymptotic expansions Theory of distributions (Functional analysis) Asymptotische Entwicklung (DE-588)4112609-9 gnd |
| topic_facet | Asymptotic expansions Theory of distributions (Functional analysis) Asymptotische Entwicklung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009757980&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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