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The university series in higher mathematics

Principal Functions

Authors: Rodin, B., Sario, L.

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About this book

During the decade and a half that has elapsed since the intro­ duction of principal functions (Sario [8 J), they have become impor­ tant tools in an increasing number of branches of modern mathe­ matics. The purpose of the present research monograph is to systematically develop the theory of these functions and their ap­ plications on Riemann surfaces and Riemannian spaces. Apart from brief background information (see below), nothing contained in this monograph has previously appeared in any other book. The basic idea of principal functions is simple: Given a Riemann surface or a Riemannian space R, a neighborhood A of its ideal boundary, and a harmonic function s on A, the principal function problem consists in constructing a harmonic function p on all of R which imitates the behavior of s in A. Here A need not be connected, but may include neighborhoods of isolated points deleted from R. Thus we are dealing with the general problem of constructing harmonic functions with given singularities and a prescribed behavior near the ideal boundary. The function p is called the principal function corresponding to the given A, s, and the mode of imitation of s by p. The significance of principal functions is in their versatility.

Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-1-4684-8038-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $109.00
price for USA in USD
  • ISBN 978-1-4684-8040-5
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Principal Functions
Authors
Series Title
The university series in higher mathematics
Copyright
1968
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4684-8038-2
DOI
10.1007/978-1-4684-8038-2
Softcover ISBN
978-1-4684-8040-5
Edition Number
1
Number of Pages
XVIII, 348
Number of Illustrations
1 b/w illustrations
Additional Information
Originally published by Van Nostrand
Topics

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