Expansions in terms of heat polynomials and associated functions

Expansions in terms of heat polynomials and associated functions
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Trans. Amer. Math. Soc. 92 (1959), 220-266

DOI: https://doi.org/10.1090/S0002-9947-1959-0107118-2

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References

Sur l’équation

et la théorie de la chaleur

Higher transcendental functions

Tables of integral transforms

Entire functions

Jerome Blackman, The inversion of solutions of the heat equation for the infinite rod, Duke Math. J. 19 (1952), 671–682. MR 51415
Maxime Bôcher, On the regions of convergence of power-series which represent two-dimensional harmonic functions, Trans. Amer. Math. Soc. 10 (1909), no. 2, 271–278. MR 1500838, DOI 10.1090/S0002-9947-1909-1500838-2

Lectures on Cauchy’s problem in linear partial differential equations

Einar Hille, A class of reciprocal functions, Ann. of Math. (2) 27 (1926), no. 4, 427–464. MR 1502747, DOI 10.2307/1967695
Einar Hille, Functional Analysis and Semi-Groups, American Mathematical Society Colloquium Publications, Vol. 31, American Mathematical Society, New York, 1948. MR 0025077
I. I. Hirschman and D. V. Widder, The convolution transform, Princeton University Press, Princeton, N. J., 1955. MR 0073746
P. C. Rosenbloom and D. V. Widder, A temperature function which vanishes initially, Amer. Math. Monthly 65 (1958), 607–609. MR 100717, DOI 10.2307/2309117
P. C. Rosenbloom, Linear equations of parabolic type with constant coefficients, Contributions to the theory of partial differential equations, Annals of Mathematics Studies, no. 33, Princeton University Press, Princeton, N.J., 1954, pp. 191–200. MR 0067319

Sur les classes quasianalytiques des solutions des équations aux dérivées partielles du type parabolique

The theory of Fourier integrals

Antoni Zygmund, Trigonometrical series, Chelsea Publishing Co., New York, 1952. 2nd ed. MR 0076084