A Distributional Approach to Asymptotics

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 contentsPreface1. Basic Results in Asymptotics2. Introduction to the Theory of Distributions3. A Distributional Theory for Asymptotic Expansions4. The Asymptotic Expansion of Multi-Dimensional Generalized Functions5. The Asymptotic Expansion of Certain Series Considered by Ramamujan6. The Cesaro Behavior of Distributions7. Series of Dirac Delta FunctionsReferencesIndex