The development of complex analysis is based on issues related to holomorphic continuation and holomorphic approximation. This volume presents a unified view of these topics in finite and infinite dimensions. A high-level tutorial in pure and applied mathematics, its prerequisites include a familiari... read more
See Sample Pages! Click here to look inside this book.
Customers who bought this book also bought:
Our Editors also recommend:
Elementary Real and Complex Analysis by Georgi E. Shilov 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.
A Second Course in Complex Analysis by William A. Veech Geared toward upper-level undergraduates and graduate students, this clear, self-contained treatment of important areas in complex analysis is chiefly classical in content and emphasizes geometry of complex mappings. 1967 edition.
Banach Spaces of Analytic Functions by Kenneth Hoffman This rigorous investigation of Hardy spaces and the invariant subspace problem is suitable for advanced undergraduates and graduates, covering complex functions, harmonic analysis, and functional analysis. 1962 edition.
A First Look at Numerical Functional Analysis by W. W. Sawyer Text by renowned educator shows how problems in numerical analysis lead to concepts of functional analysis. Topics include Banach and Hilbert spaces, contraction mappings, convergence, differentiation and integration, and Euclidean space. 1978 edition.
Complex Analysis with Applications by Richard A. Silverman The basics of what every scientist and engineer should know, from complex numbers, limits in the complex plane, and complex functions to Cauchy's theory, power series, and applications of residues. 1974 edition.
Conformal Mapping on Riemann Surfaces by Harvey Cohn Lucid, insightful exploration reviews complex analysis, introduces Riemann manifold, shows how to define real functions on manifolds, and more. Perfect for classroom use or independent study. 344 exercises. 1967 edition.
Foundations of Modern Analysis by Avner Friedman Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Detailed analyses. Problems. Bibliography. Index.
Introduction to Real Analysis by Michael J. Schramm This text forms a bridge between courses in calculus and real analysis. Suitable for advanced undergraduates and graduate students, it focuses on the construction of mathematical proofs. 1996 edition.
Foundations of Analysis: Second Edition by David F Belding, Kevin J Mitchell Unified and highly readable, this introductory approach develops the real number system and the theory of calculus, extending its discussion of the theory to real and complex planes. 1991 edition.
Complex Variables: Second Edition by Robert B. Ash, W. P. Novinger Suitable for advanced undergraduates and graduate students, this newly revised treatment covers Cauchy theorem and its applications, analytic functions, and the prime number theorem. Numerous problems and solutions. 2004 edition.
Analysis in Euclidean Space by Kenneth Hoffman Developed for a beginning course in mathematical analysis, this text focuses on concepts, principles, and methods, offering introductions to real and complex analysis and complex function theory. 1975 edition.
Function Theory on Planar Domains: A Second Course in Complex Analysis by Stephen D. Fisher This treatment of complex analysis focuses on function theory on a finitely connected planar domain. It emphasizes domains bounded by a finite number of disjoint analytic simple closed curves. 1983 edition.
Fourier Analysis in Several Complex Variables by Leon Ehrenpreis Suitable for advanced undergraduates and graduate students, this text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations. 1970 edition.
Advanced Calculus: An Introduction to Classical Analysis by Louis Brand A course in analysis that focuses on the functions of a real variable, this text introduces the basic concepts in their simplest setting and illustrates its teachings with numerous examples, theorems, and proofs. 1955 edition.
Real Analysis by Gabriel Klambauer Concise in treatment and comprehensive in scope, this text for graduate students introduces contemporary real analysis with a particular emphasis on integration theory. Includes exercises. 1973 edition.
Applied Nonstandard Analysis by Prof. Martin Davis This applications-oriented text assumes no knowledge of mathematical logic in its development of nonstandard analysis techniques and their applications to elementary real analysis and topological and Hilbert space. 1977 edition.
Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis by Felix Klein Graphical and geometrically perceptive methods enliven a distinguished mathematician's treatment of arithmetic, algebra, and analysis. Topics include calculating with natural numbers, complex numbers, goniometric functions, and infinitesimal calculus. 1932 edition. Includes 125 figures.
Counterexamples in Analysis by Bernard R. Gelbaum, John M. H. Olmsted These counterexamples deal mostly with the part of analysis known as "real variables." Covers the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, functions of 2 variables, plane sets, more. 1962 edition.
Applied Functional Analysis by D.H. Griffel This introductory text examines applications of functional analysis to mechanics, fluid mechanics, diffusive growth, and approximation. Covers distribution theory, Banach spaces, Hilbert space, spectral theory, Frechet calculus, Sobolev spaces, more. 1985 edition.
Mathematics: Its Content, Methods and Meaning by A. D. Aleksandrov, A. N. Kolmogorov, M. A. Lavrent’ev 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.
Elements of the Theory of Functions and Functional Analysis by A. N. Kolmogorov, S. V. Fomin Advanced-level text, now available in a single volume, discusses metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque intervals, Hilbert space, more. Exercises. 1957 edition.
Complex Variables: Second Edition by Stephen D. Fisher Topics include the complex plane, basic properties of analytic functions, analytic functions as mappings, analytic and harmonic functions in applications, transform methods. Hundreds of solved examples, exercises, applications. 1990 edition. Appendices.
Functional Analysis by George Bachman, Lawrence Narici Text covers introduction to inner-product spaces, normed, metric spaces, and topological spaces; complete orthonormal sets, the Hahn-Banach Theorem and its consequences, and many other related subjects. 1966 edition.
Ordinary Differential Equations in the Complex Domain by Einar Hille Graduate-level text offers full treatments of existence theorems, representation of solutions by series, theory of majorants, dominants and minorants, questions of growth, much more. Includes 675 exercises. Bibliography.
Elementary Functional Analysis by Georgi E. Shilov Introductory text covers basic structures of mathematical analysis (linear spaces, metric spaces, normed linear spaces, etc.), differential equations, orthogonal expansions, Fourier transforms, and more. Includes problems with hints and answers. Bibliography. 1974 edition.
Real Analysis by Norman B. Haaser, Joseph A. Sullivan Clear, accessible text for 1st course in abstract analysis. Explores sets and relations, real number system and linear spaces, normed spaces, Lebesgue integral, approximation theory, Banach fixed-point theorem, Stieltjes integrals, more. Includes numerous problems.
Functional Analysis by Frigyes Riesz, Béla Sz.-Nagy Classic exposition of modern theories of differentiation and integration and principal problems and methods of handling integral equations and linear functionals and transformations. 1955 edition.
Introductory Complex Analysis by Richard A. Silverman Shorter version of Markushevich's Theory of Functions of a Complex Variable, appropriate for advanced undergraduate and graduate courses in complex analysis. More than 300 problems, some with hints and answers. 1967 edition.
Introductory Real Analysis by A. N. Kolmogorov, S. V. Fomin, Richard A. Silverman Comprehensive, elementary introduction to real and functional analysis covers basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, more. 1970 edition.
Product Description:
The development of complex analysis is based on issues related to holomorphic continuation and holomorphic approximation. This volume presents a unified view of these topics in finite and infinite dimensions. A high-level tutorial in pure and applied mathematics, its prerequisites include a familiarity with the basic properties of holomorphic functions, the principles of Banach and Hilbert spaces, and the theory of Lebesgue integration. The four-part treatment begins with an overview of the basic properties of holomorphic mappings and holomorphic domains in Banach spaces. The second section explores differentiable mappings, differentiable forms, and polynomially convex compact sets, in which the results are applied to the study of Banach and Fréchet algebras. Subsequent sections examine plurisubharmonic functions and pseudoconvex domains in Banach spaces, along with Riemann domains and envelopes of holomorphy. In addition to its value as a text for advanced graduate students of mathematics, this volume also functions as a reference for researchers and professionals.
Reprint of the North-Holland Press, Amsterdam, 1986 edition.
This book was printed in the United States of America.
Dover books are made to last a lifetime. Our US book-manufacturing partners produce the highest quality books in the world and they create jobs for our fellow citizens. Manufacturing in the United States also ensures that our books are printed in an environmentally friendly fashion, on paper sourced from responsibly managed forests.
