Lectures on entire functions

Abstract

Part I. Entire Functions of Finite Order: Growth of entire functions Main integral formulas for functions analytic in a disk Some applications of the Jensen formula Factorization of entire functions of finite order The connection between the growth of an entire function and the distribution of its zeros Theorems of Phragmen and Lindelof Subharmonic functions The indicator function The Polya Theorem Applications of the Polya Theorem Lower bounds for analytic and subharmonic functions Entire functions with zeros on a ray Entire functions with zeros on a ray (continuation) Part II. Entire Functions of Exponential Type: Integral representation of functions analytic in the half-plane The Hayman Theorem Functions of class $C$ and their applications Zeros of functions of class $C$ Completeness and minimality of system of exponential functions in $L^2(0,a)$ Interpolation by entire functions of exponential type Interpolation by entire functions of the spaces $L_\pi$ and $B_\pi$ Sin-type functions Riesz bases formed by exponential functions in $L^2(-\pi,\pi)$ Completeness of the eigenfunction system of a quadratic operator pencil Part III. Some Additional Problems of the Theory of Entire Functions: Carleman's and R. Nevanlinna's formulas and their applications Uniqueness problems for Fourier transforms and for infinitely-differentiable functions The Matsaev Theorem on the growth of entire functions admitting a lower bound Entire functions of the class $P$ S. N. Bernstein's inequality for entire functions of exponential type and its generalizations Bibliography Author index Subject index.