The Fourier Integral and Certain of Its ApplicationsThe book is concerned principally with the Plancherel and Tauber theories as modified by other workers in the field, notably Wiener himself. Based on a course of lectures delivered at the University of Cambridge in 1932, it is divided into three separate groups of ideas. The first group deals with the Fourier transform and the Plancherel theorem. The second group treats the notion of an absolutely convergent Fourier series and of a Tauberian theorem. In the last group, Wiener deals with the concept of the spectrum. The final chapter is a lucid eposition of general harmonic analysis. |
Contents
Preface page ix | 1 |
The Properties of the Lebesgue Integral | 4 |
The RieszFischer Theorem | 27 |
Copyright | |
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absolutely convergent algebra APPLICATIONS E FOURIER argument belongs to L1 bounded calculus coefficients complete the proof const converges absolutely defined denumerable set e-ius e-iux dx eiux equivalent established exists finite interval finite number finite range fn(x follows FOURIER INTEGRAL Fourier series Fourier transform function f(x Hence Index infinite k₁ Konrad Knopp L₁ L₂ Lambert series Lebesgue integral lemma let us notice let us put lim lim lim sup limited total variation linear M₁ mathematical measurable function Minkowski inequality modulus non-negative normal set null set number of f(x Paperbound periodic functions pertaining Plancherel theorem polynomial proof of theorem proposition real numbers Riemann Riesz-Fischer theorem sequence step-function Tauberian theorem theorem 15 THEORY OF FUNCTIONS translation number uniformly values vanish variable zero αξ αξε δη ίξ λα λη ΣΛ ψη