On Fourier Transforms of the Class Wσ

Abstract

This note is concerned with a theorem of Plancherel for Fourier transforms which corresponds to the Parseval theorem for Fourier series. By Wσ we denote the class of integral functions {f(z)} which are of exponential type σ and such that each of the functions {f(x)} belongs to L² (-∞, ∞) for values of z = x on the real axis.