**Translations of Mathematical Monographs**

1992;
188 pp;
Hardcover

MSC: Primary 32;
**Print ISBN: 978-0-8218-4560-8
Product Code: MMONO/103**

List Price: $97.00

Individual Member Price: $77.60

# Multidimensional Residues and Their Applications

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*A. K. Tsikh*

The technique of residues is known for its many applications in different branches of mathematics. Tsikh's book presents a systematic account of residues associated with holomorphic mappings and indicates many applications. The book begins with preliminaries from the theory of analytic sets, together with material from algebraic topology that is necessary for the integration of differential forms over chains. Tsikh then presents a detailed study of residues associated with mappings that preserve dimension (local residues). Local residues are applied to algebraic geometry and to problems connected with the investigation and calculation of double series and integrals. There is also a treatment of residues associated with mappings that reduce dimension—that is, residues of semimeromorphic forms, connected with integration over tubes around nondiscrete analytic sets.

#### Table of Contents

# Table of Contents

## Multidimensional Residues and Their Applications

#### Readership

Research mathematicians.

#### Reviews

Well written and more easy to read than have been previous publications on the subject; it is a well balanced account of theory and applications. It is an excellent reference book for research in complex analysis, algebraic geometry and PDEs.

-- Bulletin of the London Mathematical Society

The book will be useful to researchers in complex analysis, and is acceptable for graduate students.

-- Zentralblatt MATH