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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Principal Functions

Principal Functions

Rodin, B.
Sario, L.
Nakai, M.

Paperback

Series: The University Higher Mathematics

CalculusGeneral GardeningGeneral Mathematics

ISBN10: 1468480405
ISBN13: 9781468480405
Publisher: Springer
Published: Jul 27 2012
Pages: 348
Weight: 1.08
Height: 0.76 Width: 6.00 Depth: 9.00
Language: English
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.

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