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The application of quadratic forms in an infinity of variables to boundary problems in partial differential equations

Published online by Cambridge University Press:  24 October 2008

S. W. P. Steen
S. W. P. Steen
Affiliation:
Christ's College
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Extract

The object of this paper is to find the characteristic functions and the characteristic numbers of the partial differential equation

valid in a domain G, and where on Γ, the boundary of G. The method employed is to transform two quadratic forms to their common self-conjugate “triangle“ of reference. The solution to the problem is given by this method in a simple manner, without the use of the integral equation theory, or the use of minimal sequences.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 28 , Issue 1 , January 1932 , pp. 23 - 34
Copyright
Copyright © Cambridge Philosophical Society 1932

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References

* Courant-Hilbert, , Methoden der mathematischen Physik, Ch. 6.Google Scholar

† The method of this paragraph is obtained from Hilbert, , Grundzüge einer allgemeine Theorie der linearen Integralgleichungen, pp. 147et seq.Google Scholar

* When , hence |x i| < √K.

* By this we mean that every point of C 1′ is at an equal distance δ from C 1, and that C 1′ has no double points.

* Courant-Hilbert, loc. cit., Ch. 6, p. 328.