Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-18T21:05:49.539Z Has data issue: false hasContentIssue false
  • English
  • Français

Homogeneous solutions of the generalized heat equation

Part of: Parabolic equations and systems Nontrigonometric harmonic analysis

Published online by Cambridge University Press:  09 April 2009

E. Kochneff
E. Kochneff
Affiliation:
Department of Mathematics Eastern Washington UniversityCheney WA 99004USA e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We discuss expansions of solutions of the generalized heat equation which have a singularity at zero in terms of two sequences of homogeneous solutions.

MSC classification

Secondary: 35K05: Heat equation 42C99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 62 , Issue 1 , February 1997 , pp. 13 - 45
Copyright
Copyright © Australian Mathematical Society 1997

References

[1]Bragg, L. R., ‘Radial heat polynomials and related functions’, Trans. Amer. Math. Soc. 119 (1965), 270–290.CrossRefGoogle Scholar
[2]Erdelyi, A., Quart. J. Math. Oxford Ser. (2) 9 (1938), 196–198.Google Scholar
[3]Hadamard, J., Lectures on Cauchy's problem in linear partial differential equations (Dover, New York, 1952).Google Scholar
[4]Haimo, D. T., ‘Expansions in terms of generalized heat polynomials and of their Appell transforms’, J. Appl. Math. Mech. 15 (1966), 735–758.Google Scholar
[5], ‘Homogeneous generalized temperatures’, SIAM J. Math. Anal. 11 (1980), 473–478.CrossRefGoogle Scholar
[6]Kochneff, E. and Sagher, Y., ‘The Appell transform and the semigroup property for temperatures’, J. Austral. Math. Soc. (Series A) 60 (1996), 109–117.CrossRefGoogle Scholar
[7]Krall, A. and Morton, R., ‘Distributional weight functions for orthogonal polynomials’, SIAM J. Math. Anal. 9 (1978), 604–626.Google Scholar
[8]Lebedev, N. N., Special functions and their applications (Prentice-Hall, New Jersey, 1965).CrossRefGoogle Scholar
[9]Rosenbloom, P. C. and Widder, D. V., [Expansions in terms of heat polynomials and associated functions’, Trans. Amer. Math. Soc. 92 (1959), 604–626.CrossRefGoogle Scholar
[10]Szego, G., Orthogonal polynomials, Amer. Math. Soc. Colloq. Pub. 23 (Amer. Math. Soc., Providence, 1979).Google Scholar