The Fourier Integral and Certain of its Applications

Norbert Wiener

doi:10.1017/CBO9780511662492

The book was written from lectures given at the University of Cambridge and maintains throughout a high level of rigour whilst remaining a highly readable and lucid account. Topics covered include the Planchard theory of the existence of Fourier transforms of a function of L2 and Tauberian theorems. The influence of G. H. Hardy is apparent from the presence of an application of the theory to the prime number theorems of Hadamard and de la Vallee Poussin. Both pure and applied mathematicians will welcome the reissue of this classic work. For this reissue, Professor Kahane's Foreword briefly describes the genesis of Wiener's work and its later significance to harmonic analysis and Brownian motion.

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The Fourier Integral and Certain of its Applications

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

Foreword
pp ix-xiv

Preface
pp xv-xviii

INTRODUCTION
pp 1-45

CHAPTER I - PLANCHEREL'S THEOREM
pp 46-71

CHAPTER II - THE GENERAL TAUBERIAN THEOREM
pp 72-103

CHAPTER III - SPECIAL TAUBERIAN THEOREMS
pp 104-149

CHAPTER IV - GENERALIZED HARMONIC ANALYSIS
pp 150-199

Bibliography
pp 200-201

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The Fourier Integral and Certain of its Applications

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