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Birkhäuser

A Distributional Approach to Asymptotics

Theory and Applications

  • Textbook
  • © 2002

Overview

Authors:
  1. Ricardo Estrada

    1. Escuela de Matemática, Universidad de Costa Rica, San José, Costa Rica

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    You can also search for this author in PubMed   Google Scholar

  2. Ram P. Kanwal

    1. Department of Mathematics, Pennsylvania State University, University Park, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Birkhäuser Advanced Texts Basler Lehrbücher (BAT)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xv
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  2. Basic Results in Asymptotics

    • Ricardo Estrada, Ram P. Kanwal
    Pages 1-52

  3. Introduction to the Theory of Distributions

    • Ricardo Estrada, Ram P. Kanwal
    Pages 53-105

  4. A Distributional Theory for Asymptotic Expansions

    • Ricardo Estrada, Ram P. Kanwal
    Pages 107-186

  5. The Asymptotic Expansion of Multidimensional Generalized Functions

    • Ricardo Estrada, Ram P. Kanwal
    Pages 187-248

  6. The Asymptotic Expansion of Certain Series Considered by Ramanujan

    • Ricardo Estrada, Ram P. Kanwal
    Pages 249-296

  7. Cesàro Behavior of Distributions

    • Ricardo Estrada, Ram P. Kanwal
    Pages 297-396

  8. Series of Dirac Delta Functions

    • Ricardo Estrada, Ram P. Kanwal
    Pages 397-432

  9. Back Matter

    Pages 433-454
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Keywords

About this book

"...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) 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. Key features of this significantly expanded and revised second edition: * addition of a new chapter and many new sections * wide range of topics covered, including the Ces.ro behavior of distributions and their connections to asymptotic analysis, the study of time-domain asymptotics, and the use of series of Dirac delta functions to solve boundary value problems * novel approach detailing the interplay between underlying theories of asymptotic analysis and generalized functions * extensive examples and exercises at the end of each chapter * comprehensive bibliography and index This work is an excellent tool for the classroom and an invaluable self-study resource that will stimulate application of asymptotic

Reviews

"This is not just a ‘Second Edition’ of some monograph in the usual sense, but a revised and largely expanded version of Asymptotic Analysis: A Distributional Approach (1994) by the same authors…. A completely new chapter on the Cesáro behavior of distributions has been added; moreover there are several new sections, among them respective problem sections at the end of each chapter. Finally, a large number of recent results and additional examples have been included…. Even more than its predecessor, this book presents an interesting and carefully written introduction into the theory and applications of asymptotic analysis based on distribution theory."

—MONATSHEFTE FÜR MATHEMATIK (Review of the Second Edition)

"The authors of this remarkable book are among the very few that 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 First 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 REVIEW (Review of the First Edition)

Authors and Affiliations

  • Escuela de Matemática, Universidad de Costa Rica, San José, Costa Rica

    Ricardo Estrada

  • Department of Mathematics, Pennsylvania State University, University Park, USA

    Ram P. Kanwal

Bibliographic Information

  • Book Title: A Distributional Approach to Asymptotics

  • Book Subtitle: Theory and Applications

  • Authors: Ricardo Estrada, Ram P. Kanwal

  • Series Title: Birkhäuser Advanced Texts Basler Lehrbücher

  • DOI: https://doi.org/10.1007/978-0-8176-8130-2

  • Publisher: Birkhäuser Boston, MA

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Boston 2002

  • Hardcover ISBN: 978-0-8176-4142-9Published: 08 February 2002

  • Softcover ISBN: 978-1-4612-6410-1Published: 05 September 2012

  • eBook ISBN: 978-0-8176-8130-2Published: 08 September 2012

  • Series ISSN: 1019-6242

  • Series E-ISSN: 2296-4894

  • Edition Number: 2

  • Number of Pages: XV, 454

  • Additional Information: Originally published with the title: Asymptomic Analysis: A Distributional Approach

  • Topics: Analysis, Applications of Mathematics, Statistical Theory and Methods

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