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## The Theory of Functions of a Real Variable and the Theory of Fourier s Series

## Theory of Functions of a Real Variable

Long out-of-print volume by a prominent Soviet mathematician presents a thorough examination of the theory of functions of a real variable. Intended for advanced undergraduates and graduate students of mathematics. 1955 and 1960 editions.
## Theory of Approximation of Functions of a Real Variable

Excellent graduate-level monograph investigates relationship between various structural properties of real functions and the character of possible approximations to them by polynomials and other functions of simple construction. Based on classical approximation theorem of Weierstrass, P. L. Chebyshevâ€™s concept of the best approximation, converse theorem of S. N. Bernstein on existence of a function with a given sequence of best approximations. Each chapter includes problems and theorems supplementing main text. 1963 edition. Bibliography.
## Elementary Theory of Analytic Functions of One or Several Complex Variables

Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition.
## The theory of functions of a real variable and the theory of Fourier s series 1

## Elements of the Theory of Functions

Well-known book provides a clear, concise review of complex numbers and their geometric representation; linear functions and circular transformations; sets, sequences, and power series; analytic functions and conformal mapping; and elementary functions. 1952 edition.
## Methods of the Theory of Functions of Many Complex Variables

This systematic exposition outlines the fundamentals of the theory of single sheeted domains of holomorphy. It further illustrates applications to quantum field theory, the theory of functions, and differential equations with constant coefficients. Students of quantum field theory will find this text of particular value. The text begins with an introduction that defines the basic concepts and elementary propositions, along with the more salient facts from the theory of functions of real variables and the theory of generalized functions. Subsequent chapters address the theory of plurisubharmonic functions and pseudoconvex domains, along with characteristics of domains of holomorphy. These explorations are further examined in terms of four types of domains: multiple-circular, tubular, semitubular, and Hartogs' domains. Surveys of integral representations focus on the Martinelli-Bochner, Bergman-Weil, and Bochner representations. The final chapter is devoted to applications, particularly those involved in field theory. It employs the theory of generalized functions, along with the theory of functions of several complex variables.
## General Theory of Functions and Integration

Uniting a variety of approaches to the study of integration, a well-known professor presents a single-volume "blend of the particular and the general, of the concrete and the abstract." 1966 edition.
## Complex Variables

Contents include calculus in the plane; harmonic functions in the plane; analytic functions and power series; singular points and Laurent series; and much more. Numerous problems and solutions. 1972 edition.
## Elementary Real and Complex Analysis

Excellent undergraduate-level text offers coverage of real numbers, sets, metric spaces, limits, continuous functions, much more. Each chapter contains a problem set with hints and answers. 1973 edition.
## Selected Topics in the Classical Theory of Functions of a Complex Variable

Elegant and concise, this text explores properties of meromorphic functions, Picard theorem, harmonic and subharmonic functions, applications, and boundary behavior of the Riemann mapping function for simply connected Jordan regions. 1962 edition.
## Mathematics

Major survey offers comprehensive, coherent discussions of analytic geometry, algebra, differential equations, calculus of variations, functions of a complex variable, prime numbers, linear and non-Euclidean geometry, topology, functional analysis, more. 1963 edition.
## Integration Measure and Probability

Introductory treatment develops the theory of integration in a general context, making it applicable to other branches of analysis. More specialized topics include convergence theorems and random sequences and functions. 1963 edition.
## An Introduction to Mathematical Analysis

Dealing chiefly with functions of a single real variable, this text by a distinguished educator introduces limits, continuity, differentiability, integration, convergence of infinite series, double series, and infinite products. 1963 edition.
## Elements of Real Analysis

Classic text explores intermediate steps between basics of calculus and ultimate stage of mathematics -- abstraction and generalization. Covers fundamental concepts, real number system, point sets, functions of a real variable, Fourier series, more. Over 500 exercises.