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On discrete harmonic functions

Published online by Cambridge University Press:  24 October 2008

H. A. Heilbronn
H. A. Heilbronn
Affiliation:
The Royal FortBristol 8
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Extract

A function f(x1, x2) of two real variables x1, x2 which are restricted to rational integers will be called discrete harmonic (d.h.) if it satisfies the difference equation

This equation can be considered as the direct analogue either of the differential equation

or of the integral equation

in the notation normally employed to harmonic functions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 45 , Issue 2 , April 1949 , pp. 194 - 206
Copyright
Copyright © Cambridge Philosophical Society 1949

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