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The kernel function and conformal mapping
 
The kernel function and conformal mapping
eBook ISBN:  978-1-4704-1232-6
Product Code:  SURV/5.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
The kernel function and conformal mapping
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The kernel function and conformal mapping
eBook ISBN:  978-1-4704-1232-6
Product Code:  SURV/5.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 51950; 257 pp
    MSC: Primary 30;

    The Kernel Function and Conformal Mapping by Stefan Bergman is a revised edition of The Kernel Function. The author has made extensive changes in the original volume. The present book will be of interest not only to mathematicians, but also to engineers, physicists, and computer scientists. The applications of orthogonal functions in solving boundary value problems and conformal mappings onto canonical domains are discussed; and publications are indicated where programs for carrying out numerical work using high-speed computers can be found.

    The unification of methods in the theory of functions of one and several complex variables is one of the purposes of introducing the kernel function and the domains with a distinguished boundary. This approach has been extensively developed during the last two decades. This second edition of Professor Bergman's book reviews this branch of the theory including recent developments not dealt with in the first edition. The presentation of the topics is simple and presupposes only knowledge of an elementary course in the theory of analytic functions of one variable.

    Readership

    Graduate students and research mathematicians interested in analysis.

  • Table of Contents
     
     
    • Chapters
    • I. Orthogonal functions
    • II. The kernel function and associated minimum problems
    • III. The invariant metric and the method of the minimum integral
    • IV. Kernel functions and Hilbert space
    • V. Representation of the classical domain functions
    • VI. Canonical conformal transformations
    • VII. Orthogonalization over the boundary
    • VIII. Variational methods
    • IX. Existence proofs
    • X. Partial differential equations
    • XI. Functions of two complex variables and pseudo-conformal mappings
    • XII. Generalization of potential-theoretical and certain subclasses of functions
  • 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: 51950; 257 pp
MSC: Primary 30;

The Kernel Function and Conformal Mapping by Stefan Bergman is a revised edition of The Kernel Function. The author has made extensive changes in the original volume. The present book will be of interest not only to mathematicians, but also to engineers, physicists, and computer scientists. The applications of orthogonal functions in solving boundary value problems and conformal mappings onto canonical domains are discussed; and publications are indicated where programs for carrying out numerical work using high-speed computers can be found.

The unification of methods in the theory of functions of one and several complex variables is one of the purposes of introducing the kernel function and the domains with a distinguished boundary. This approach has been extensively developed during the last two decades. This second edition of Professor Bergman's book reviews this branch of the theory including recent developments not dealt with in the first edition. The presentation of the topics is simple and presupposes only knowledge of an elementary course in the theory of analytic functions of one variable.

Readership

Graduate students and research mathematicians interested in analysis.

  • Chapters
  • I. Orthogonal functions
  • II. The kernel function and associated minimum problems
  • III. The invariant metric and the method of the minimum integral
  • IV. Kernel functions and Hilbert space
  • V. Representation of the classical domain functions
  • VI. Canonical conformal transformations
  • VII. Orthogonalization over the boundary
  • VIII. Variational methods
  • IX. Existence proofs
  • X. Partial differential equations
  • XI. Functions of two complex variables and pseudo-conformal mappings
  • XII. Generalization of potential-theoretical and certain subclasses of functions
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.