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• [2] H. Bateman and A. Erdèlyi, Higher transcendental functions, vol. II, 1953.
• [3] -, Tables of integral transforms, vol. I, 1954.
• [4] R. P. Boas, Entire functions, 1954.
• [5] Jerome Blackman, The inversion of solutions of the heat equation for the infinite rod, Duke Math. J. 19 (1952), 671–682. MR 51415
• [6] 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, https://doi.org/10.1090/S0002-9947-1909-1500838-2
• [7] J. Hadamard, Lectures on Cauchy's problem in linear partial differential equations, 1923.
• [8] Einar Hille, A class of reciprocal functions, Ann. of Math. (2) 27 (1926), no. 4, 427–464. MR 1502747, https://doi.org/10.2307/1967695
• [9] Einar Hille, Functional Analysis and Semi-Groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, New York, 1948. MR 0025077
• [10] I. I. Hirschman and D. V. Widder, The convolution transform, Princeton University Press, Princeton, N. J., 1955. MR 0073746
• [11] P. C. Rosenbloom and D. V. Widder, A temperature function which vanishes initially, Amer. Math. Monthly 65 (1958), 607–609. MR 100717, https://doi.org/10.2307/2309117
• [12] 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
• [13] S. Täcklind, Sur les classes quasianalytiques des solutions des équations aux dérivées partielles du type parabolique, Nova Acta Soc. Sci. Upsal. Ser. IV, vol. 10 (1936) pp. 1-56.
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Bibliography

[1]

P. Appell, Sur l'équation et la théorie de la chaleur, J. Math Pures Appl. vol. 8 (1892) pp. 187-216.

[2]

H. Bateman and A. Erdèlyi, Higher transcendental functions, vol. II, 1953.

[3]

-, Tables of integral transforms, vol. I, 1954.

[4]

R. P. Boas, Entire functions, 1954.

[5]

J. Blackman, The inversion of solutions of the heat equation for the infinite rod, Duke Math. J. vol. 19 (1952) pp. 671-682. MR 0051415 (14:475c)

[6]

M. Bôcher, On the regions of convergence of power-series which represent two-dimensional harmonic functions, Trans. Amer. Math. Soc., vol. 10 (1909) pp. 271-278. MR 1500838

[7]

J. Hadamard, Lectures on Cauchy's problem in linear partial differential equations, 1923.

[8]

E. Hille, A class of reciprocal functions, Ann. of Math. vol. 27 (1926) pp. 427-468. MR 1502747

[9]

-, Functional analysis and semi-groups, Amer. Math. Soc. Colloquium Publications, vol. 31, 1948. MR 0025077 (9:594b)

[10]

I. I. Hirschman and D. V. Widder, The convolution transform, 1955. MR 0073746 (17:479c)

[11]

P. C. Rosenbloom and D. V. Widder, A temperature function which vanishes initially, Amer. Math. Monthly vol. 65 (1958) pp. 607-609. MR 0100717 (20:7146)

[12]

P. C. Rosenbloom, Linear equations of parabolic type with constant coefficients, Annals of Mathematics Studies, no. 33, 1954, pp. 191-200. MR 0067319 (16:709d)

[13]

S. Täcklind, Sur les classes quasianalytiques des solutions des équations aux dérivées partielles du type parabolique, Nova Acta Soc. Sci. Upsal. Ser. IV, vol. 10 (1936) pp. 1-56.

[14]

E. C. Titchmarsh, The theory of Fourier integrals, 1937.

[15]

A. Zygmund, Trigonometrical series, 1952. MR 0076084 (17:844d)