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Multidimensional Residues and Their Applications
A. K. Tsikh
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Translations of Mathematical Monographs
1992; 188 pp; hardcover
Volume: 103
ISBN-10: 0-8218-4560-8
ISBN-13: 978-0-8218-4560-8
List Price: US$92
Member Price: US$73.60
Order Code: MMONO/103
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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.

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

Table of Contents

  • Preliminary information
  • Residues associated with mappings \(f\colon \mathbf C^n\rightarrow \mathbf C^n\) (local residues)
  • Residues associated with mappings \(f\colon \mathbf C^n\rightarrow \mathbf C^p\) (residual currents and principal values)
  • Applications to function theory and algebraic geometry
  • Applications to the calculation of double series and integrals
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