Regular Variation

by N. H. Bingham, C. M. Goldie, J. L. Teugels

Overview

Both the theory and applications of regular variation are given comprehensive coverage in this volume. In many limit theorems, regular variation is intrinsic to the result and exactly characterizes the limit behavior. The book emphasizes such characterizations, and gives a comprehensive treatment of those applications where regular variation plays an essential (rather than merely convenient) role. The authors rigorously develop the basic ideas of Karamata theory and de Haan theory including many new results and "second-order" theorems. They go on to discuss the role of regular variation in Abelian, Tauberian, and Mercerian theorems. These results are then applied in analytic number theory, complex analysis, and probability, with the aim of setting the theory in context. A widely scattered literature is thus brought together in a unified approach. With several appendices and a comprehensive list of references, analysts, number theorists, probabilitists, research workers, and graduate students will find this an invaluable and complete account of regular variation.

Product Details

ISBN-13:	9780521379434
Publisher:	Cambridge University Press
Publication date:	06/15/1989
Series:	Encyclopedia of Mathematics and its Applications , #27
Edition description:	Reprint
Pages:	516
Product dimensions:	6.14(w) x 9.21(h) x 0.98(d)

Table of Contents

Preface; Preface to the paperback edition; 1. Karamata theory; 2. Further Karamata theory; 3. De Haan theory; 4. Abelian and Tauberian theorems; 5. Mercerian theorems; 6. Applications to analytic number theory; 7. Applications to complex analysis; 8. Applications to probability theory; Appendices; References.

Editorial Reviews

"...presents a broad and variegated area of knowledge in an orderly, accessible, and yet impressive way. An opera of real analysis, so to speak." Bulletin of the American Mathematical Society

"Papers still appear in this subject and probably will continue to do so. This book may not be the last word, but it will certainly be the best for a long time to come." Mathematical Reviews

From the Publisher