Tauberian Theory: A Century of Developments (Softcover)

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LIKE NEW: This softcover book is in excellent, like-new condition. The book's pages are printed on acid-free paper.

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From the Preface: "Summability methods have been used at least since the days of Euler to assign a reasonable sum to an infinite series, whether it is convergent or not. In its simplest form, Tauberian theory deals with the problem of finding conditions under which a summable series is actually convergent. A first condition of this kind, which applies to Abel summability (the power series method), was given by Alfred Tauber in 1897. However, Tauberian theory began in earnest only around 1910 with the work of Hardy and Littlewood. Over a period of thirty years they obtained a large number of refined 'Tauberian theorems', and they gave the subject its euphonious name."

From the back cover: "Tauberian theory compares different summability methods both 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 extols 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 theorems. A large bibliography and a substantial index round out the book."

BRIEF CONTENTS

1. The Hardy-Littlewood Theorems
2. Wiener's Theory
3. Complex Tauberian Theorems
4. Karamata's Heritage: Regular Variation
5. Extensions of the Classical Theory
6. Borel Summability and General Circle Methods
7. Tauberian Remainder Theory