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Multidimensional Residues and Their Applications
 
Multidimensional Residues and Their Applications
Hardcover ISBN:  978-0-8218-4560-8
Product Code:  MMONO/103
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4514-0
Product Code:  MMONO/103.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Hardcover ISBN:  978-0-8218-4560-8
eBook: ISBN:  978-1-4704-4514-0
Product Code:  MMONO/103.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
Multidimensional Residues and Their Applications
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Multidimensional Residues and Their Applications
Hardcover ISBN:  978-0-8218-4560-8
Product Code:  MMONO/103
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4514-0
Product Code:  MMONO/103.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Hardcover ISBN:  978-0-8218-4560-8
eBook ISBN:  978-1-4704-4514-0
Product Code:  MMONO/103.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
  • Book Details
     
     
    Translations of Mathematical Monographs
    Volume: 1031992; 188 pp
    MSC: 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.

    Readership

    Research 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1031992; 188 pp
MSC: 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.

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.