Functions of Completely Regular Growth

This monograph deals with functions of completely regular growth (FCRG), ie functions that have, in some sense, good asymptotic behaviour out of an exceptional set. The theory of entire functions of completely regular growth of one variable, developed in the late 1930s, soon found applications in both mathematics and physics. Later, the theory was extended to functions in the half-plane, subharmonic functions in space, and entire functions of several variables. This volume describes this theory and presents recent developments based on the concept of weak convergence. This enables a unified approach and provides a comparatively simple presentation of the classical Levin-Pfluger theory. Emphasis is put on those classes of functions which are particularly important for applications – functions having a bounded spectrum and finite exponential sums. While aimed at research mathematicians and physicists whose work involves complex analysis and its applications, the book should also be useful to those working in some areas of radiophysics and optics.