ABSTRACT

Chapter 3 contains the background material. It is a collection of basic conceptions and classical theorems of the theory of entire functions, part of which is given without proofs. In particular, we present the Weierstrass theorem on the representation of an arbitrary entire function by an infinite product and the Hadamard theorem on the representation of a finite-order entire function by a canonical product. The classical results of Borel, Hadamard, and Lindelo´f on the connections between the growth of an entire function and the distribution of its zeros and the Jensen theorem on the counting function of zeros are also included in this chapter.