A Distributional Approach to Asymptotics: Theory and Applications

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Springer Science & Business Media, Feb 8, 2002 - Mathematics - 454 pages
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Key features of this significantly expanded second edition: - addition of several new chapters and sections, including a presentation of time-domain asymptotics needed for the understanding of wavelet theory - extensive examples and problem sets - useful bibliography and index. This book is a modern introduction to asymptotic analysis intended not only for mathematicians, but for physicists, engineers, and graduate students as well. Written by two of the leading experts in the field, the text provides readers with a firm grasp of mathematical theory, and at the same time demonstrates applications in areas such as differential equations, quantum mechanics, noncommutative geometry, and number theory. "...The authors of this remarkable book are among the very few who have faced up to the challenge of explaining what an asymptotic expansion is, and of systematizing the handling of asymptotic series. The idea of using distributions is an original one, and we recommend that you read the book...[it] should be on your bookshelf if you are at all interested in knowing what an asymptotic series is." ¿ "The Bulletin of Mathematics Books" (Review of the 1st edition) "...The book is a valuable one, one that many applied mathematicians may want to buy. The authors are undeniably experts in their field...most of the material has appeared in no other book." ¿ "SIAM News" (Review of the 1st edition) Table of contents Preface 1. Basic Results in Asymptotics 2. Introduction to the Theory of Distributions 3. A Distributional Theory for Asymptotic Expansions 4. The Asymptotic Expansion of Multi-Dimensional Generalized Functions 5. The Asymptotic Expansion of Certain Series Considered by Ramamujan 6. The Cesaro Behavior of Distributions 7. Series of Dirac Delta Functions References Index
 

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Contents

Baslc Results ln Asymptotlcs
1
Introductlon to the Theory of Distributions
53
A Distributional Theory for Asymptotic Expansions
107
Asymptotic Expansion of Multidimensional Generalized Functions
187
Asymptotic Expansion of Certain Series Considered
249
Contents ix
297
Series of Dlrac Delta Functions
397
References 433
431
Index
447
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