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Expansions in terms of heat polynomials and associated functions


Authors: P. C. Rosenbloom and D. V. Widder
Journal: Trans. Amer. Math. Soc. 92 (1959), 220-266
MSC: Primary 41.00; Secondary 35.00
DOI: https://doi.org/10.1090/S0002-9947-1959-0107118-2
MathSciNet review: 0107118
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  • [1] P. Appell, Sur l'équation $ {\partial ^2}z/\partial {x^2} - \partial z/\partial y$ 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)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1959-0107118-2
Article copyright: © Copyright 1959 American Mathematical Society

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