Lectures On Entire Functions (translations Of Mathematical Monographs)

The aim of the monograph is to expose the main facts of the theory of entire functions and to give their applications in real and functional analysis.The general theory starts with fundamental results on the growth of entire functions of finite order, their factorization according to Hadamard's theorem, properties of the indicator, and theorems of the Phragmen-Lindelof type.Numerous applications include Riesz' bases formed by exponential functions, completeness and minimality of special systems of functions, quasianalyticity of lacunar Fourier series and infinitely differentiable functions, the Titchmarsh convolution theorem, mean-periodic functions, interpolation in spaces of entire functions, the uniqueness problem for Fourier series and infinitely differentiable functions, Bernstein's inequality for the derivative of an entire function, and some properties of Banach algebras.No special knowledge is required to read this book, except for a standard course of the theory of functions of one complex variable.The monograph will be useful for graduate students studying the theory of analytic functions, as well as for research mathematicians. For approximately 40 years, the author's Kharkov University seminar was a school for mathematicians working in analysis and a centre for active research. This monograph aims to expose the main facts of the theory of entire functions and to give their applications in real and functional analysis. Presents the fundamental results on the growth of entire functions of finite order, their factorization according to the Hadamard theorem, properties of indicator and theorems of Phragmen-Lindelof type.