As a brilliant university lecturer, B. Ya. Levin attracted a large audience of working mathematicians and of students from various levels and backgrounds. For approximately 40 years, his Kharkov University seminar was a school for mathematicians working in analysis and a center 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. The general theory starts with 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 PhragménLindelöf type. Readership Graduate students studying the theory of analytic functions and research mathematicians working in adjacent fields and applications. Reviews "Readers with some previous knowledge will experience pleasant surprises at the deft way in which the material is presented. David Drasin's excellent translation is smooth and idiomatic. It reads like a book written in English by a gifted expositor."  Zentralblatt MATH "These 28 lectures are written in the elegant form that was typical of the teaching style of B. Ya. Levin."  Mathematical Reviews "Very welcome ... superbly organised ... would form an ideal basis for an advanced course. The student is not overloaded, but each lecture contains new and interesting material."  Bulletin of the London Mathematical Society Table of Contents 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 Phragmén and Lindelöf
 Subharmonic functions
 The indicator function
 The Pólya Theorem
 Applications of the Pólya 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 representaiton of functions analytic in the halfplane
 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 \(B_\pi\)
 Sintype 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 infinitelydifferentiable 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
