With the aid of Fourier-Mellin transforms as a tool in analysis, the authors were able to attack such diverse analytic questions as those of quasi-analytic functions, Mercer's theorem on summability, Milne's integral equation of radiative equilibrium, the theorems of Münz and Szász concerning the closure of sets of powers of an argument, Titchmarsh's theory of entire functions of semi-exponential type with real negative zeros, trigonometric interpolation and developments in polynomials of the form $\sum^N_1A_ne^{i\lambda_nx}$, lacunary series, generalized harmonic analysis in the complex domain, the zeros of random functions, and many others.

Table of Contents

• Introduction
• Quasi-analytic functions
• Szász's theorem
• Certain integral expansions
• A class of singular integral equations
• Entire functions of the exponential type
• The closure of sets of complex exponential functions
• Non-harmonic Fourier series and a gap theorem
• Generalized harmonic analysis in the complex domain
• The harmonic analysis of random functions
• Bibliography
• Index