Greene Robert E., Krantz Stephen G. Function Theory of One Complex Variable
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American Mathematical Society, 2006. — 525 p.This book is a text for a first-year graduate course in complex analysis. All material usually treated in such a course is covered here, but our book is based on principles that differ somewhat from those underlying most introductory graduate texts on the subject.This third edition follows the overall plan and even the specific arrangement of topics of the second edition, but there have been substantial changes in matters of detail. A considerable number of the proofs, especially in the later chapters, have been corrected, clarified, or simplified. Many of the exercises have been revised, and in many cases the exercises have been rearranged to make for greater consistency and less duplication. The mathematical roads that this new edition follows are the same as before, but we hope that the ride is considerably smoother.
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