Problems in Real and Complex Analysis

ISBN-13: 9780387977669 / Angielski / Twarda / 1992 / 489 str.

Bernard R. Gelbaum

Opis

This text covers many principal topics in the theory of functions of a complex variable. These include, in real analysis, set algebra, measure and topology, real- and complex-valued functions, and topological vector spaces. In complex analysis, they include polynomials and power series, functions holomorphic in a region, entire functions, analytic continuation, singularities, harmonic functions, families of functions, and convexity theorems.

Spis treści

1 Set Algebra and Function Lattices.- 2 Topology, Limits, and Continuity.- 3 Real- and Complex-valued Functions.- 4 Measure and Topology.- 5 Measure Theory.- 6 Topological Vector Spaces.- 7 Elementary Theory.- 8 Functions Holomorphic in a Disc.- 9 Functions Holomorphic in a Region.- 10 Entire Functions.- 11 Analytic Continuation.- 12 Singularities.- 13 Harmonic Functions.- 14 Families of Functions.- 15 Convexity Theorems.- Symbol List.- Glossary/Index.