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Tauberian Theory

A Century of Developments

  • Jacob Korevaar

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 329)

Table of contents

  1. Front Matter
    Pages I-XV
  2. Jacob Korevaar
    Pages 1-64
  3. Jacob Korevaar
    Pages 65-115
  4. Jacob Korevaar
    Pages 117-176
  5. Jacob Korevaar
    Pages 177-234
  6. Jacob Korevaar
    Pages 235-278
  7. Jacob Korevaar
    Pages 279-341
  8. Jacob Korevaar
    Pages 343-419
  9. Back Matter
    Pages 421-486

About this book

Introduction

Tauberian theory compares summability methods for series and integrals, helps to decide when there is convergence, and provides asymptotic and remainder estimates. The author shows the development of the theory from the beginning and his expert commentary evokes the excitement surrounding the early results. He shows the fascination of the difficult Hardy-Littlewood theorems and of an unexpected simple proof, and extolls Wiener's breakthrough based on Fourier theory. There are the spectacular "high-indices" theorems and Karamata's "regular variation", which permeates probability theory. The author presents Gelfand's elegant algebraic treatment of Wiener theory and his own distributional approach. There is also a new unified theory for Borel and "circle" methods. The text describes many Tauberian ways to the prime number theorem. A large bibliography and a substantial index round out the book.

Keywords

Prime Prime number Tauberian theory asymptotic estimates prime number theorem remainder theory summability methods

Authors and affiliations

  • Jacob Korevaar
    • 1
  1. 1.KdV Mathematical InstituteUniversity of AmsterdamAmsterdamThe Netherlands

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-10225-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-05919-3
  • Online ISBN 978-3-662-10225-1
  • Series Print ISSN 0072-7830
  • Buy this book on publisher's site