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The wave, Laplace, and heat equations and related transforms

Published online by Cambridge University Press:  18 May 2009

J. W. Dettman
J. W. Dettman
Affiliation:
Oakland University, Rochester, Michigan
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This paper is concerned with three basic transforms

The first of these has been studied by Widder [1], who points out that f(t) can be interpreted as the temperature u(0, t) on the time axis, where u(x, t) is the solution of the heat equation withsymmetric initial temperature u(x, 0) = g(|x|). The second has also been studied by Widder [2], where it is pointed out that f(t) can be interpreted as the value of the harmonic function u(x, t) on the t-axis arising from the boundary data u(x, 0) = g(|x|).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 11 , Issue 2 , July 1970 , pp. 117 - 125
Copyright
Copyright © Glasgow Mathematical Journal Trust 1970

References

REFERENCES

1.Widder, D. V., Inversion of a heat transform by use of series, J. d'Analyse Math. 18 (1967), 389–413.CrossRefGoogle Scholar
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