Book Review: The Fourier Integral and Certain of its Applications

Abstract

"An elaboration of a course of fifteen lectures given at the University of Cambridge during the Lent term of 1932." "An unabridged and unaltered republication of the work originally published in 1933." The 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. Plancherel's theorem -- The general Tauberian theorem -- Special Tauberian theorems -- Generalized harmonic analysis.