Description
BIRKHAUSER A Distributional Approach To Asymptotics Theory And Applications by Ricardo Estrada, Ram P. Kanwal
"...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
Preface * 1. Basic Results in Asymptotics * 2. Introduction to the Theory of Distributions * 3. A Distributional Theory for Asymptotic Expansions * 4. Asymptotic Expansion of Multi-Dimensional Generalized Functions * 5. Asymptotic Expansion of Certain Series Considered by Ramanujan * 6. Cesaro Behavior of Distributions * 7. Series of Dirac Delta Functions * References * Index