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The wave, Laplace, and heat equations and related transforms
Glasgow mathematical journal, Tome 11 (1970) no. 2, pp. 117-125

Voir la notice de l'article provenant de la source Cambridge University Press

This paper is concerned with three basic transformsThe 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|). 
Dettman, J. W. The wave, Laplace, and heat equations and related transforms. Glasgow mathematical journal, Tome 11 (1970) no. 2, pp. 117-125. doi: 10.1017/S0017089500000963
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[1] 1.Widder, D. V., Inversion of a heat transform by use of series, J. d'Analyse Math. 18 (1967), 389–413. Google Scholar | DOI

[2] 2.Widder, D. V., A transform related to the Poisson integral for a half-plane, Duke Math. J. 33 (1966), 355–362. Google Scholar | DOI

[3] 3.Bragg, L. R. and Dettman, J. W., Related problems in partial differential equations, Bull. Amer. Math. Soc. 74 (1968), 375–378. Google Scholar | DOI

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