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Modern Real and Complex Analysis

ISBN: 978-1-118-03080-6
504 pages
February 2011
Modern Real and Complex Analysis (111803080X) cover image
Modern Real and Complex Analysis

Thorough, well-written, and encyclopedic in its coverage, this text offers a lucid presentation of all the topics essential to graduate study in analysis. While maintaining the strictest standards of rigor, Professor Gelbaum's approach is designed to appeal to intuition whenever possible. Modern Real and Complex Analysis provides up-to-date treatment of such subjects as the Daniell integration, differentiation, functional analysis and Banach algebras, conformal mapping and Bergman's kernels, defective functions, Riemann surfaces and uniformization, and the role of convexity in analysis. The text supplies an abundance of exercises and illustrative examples to reinforce learning, and extensive notes and remarks to help clarify important points.
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REAL ANALYSIS.

Fundamentals.

Integration.

Functional Analysis.

More Measure Theory.

COMPLEX ANALYSIS.

Locally Holomorphic Functions.

Harmonic Functions.

Meromorphic and Entire Functions.

Conformal Mapping.

Defective Functions.

Riemann Surfaces.

Convexity and Complex Analysis.

Several Complex Variables.

Bibliography.

Symbol List.

Glossary/Index.
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BERNARD R. GELBAUM is Professor of Mathematics at the State University of New York at Buffalo. He has previously served on the faculties of the University of Minnesota, the University of California, Irvine, and as a Fulbright Senior Scholar at University College, Galway, Ireland. He has published research in analysis and probability theory and is the author of Theorems and Counterexamples in Mathematics; Problems in Real and Complex Analysis; and Linear Algebra: Basics, Practice and Theory.
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