Hardcover ISBN:  9780821845608 
Product Code:  MMONO/103 
List Price:  $103.00 
MAA Member Price:  $92.70 
AMS Member Price:  $82.40 
Electronic ISBN:  9781470445140 
Product Code:  MMONO/103.E 
List Price:  $97.00 
MAA Member Price:  $87.30 
AMS Member Price:  $77.60 

Book DetailsTranslations of Mathematical MonographsVolume: 103; 1992; 188 ppMSC: Primary 32;
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.
ReadershipResearch mathematicians.

Table of Contents

Chapters

Chapter I. Preliminary information

Chapter II. Residues associated with mappings $f\colon \mathbf C^n\rightarrow \mathbf C^n$ (local residues)

Chapter III. Residues associated with mappings $f\colon \mathbf C^n\rightarrow \mathbf C^p$ (residual currents and principal values)

Chapter IV. Applications to function theory and algebraic geometry

Chapter V. Applications to the calculation of double series and integrals


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


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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.
Research mathematicians.

Chapters

Chapter I. Preliminary information

Chapter II. Residues associated with mappings $f\colon \mathbf C^n\rightarrow \mathbf C^n$ (local residues)

Chapter III. Residues associated with mappings $f\colon \mathbf C^n\rightarrow \mathbf C^p$ (residual currents and principal values)

Chapter IV. Applications to function theory and algebraic geometry

Chapter V. Applications to the calculation of double series and integrals

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