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Some analogies from classical analysis in the theory of heat conduction

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Bibliography

  1. Appell, P., Sur l'équation ∂2 z/∂x 2−∂z/∂y et la théorie de la chaleur. J. Math. Pures et Appl. 9, 187–216 (1892).

    Google Scholar 

  2. Blackman, J., The inversion of solutions of the heat equation for the infinite rod. Duke Math. J. 19, 671–682 (1952).

    Google Scholar 

  3. Fourier, J., The Analytic Theory of Heat. (Translation by A. Freeman). Cambridge, England: Univerity Press 1878.

    Google Scholar 

  4. Hörmander, L., Uniqueness theorems and estimates for normally hyperbolic differential equations of the second order. C. R. du 12me Congrès des Maths. Scandinaves, Lund (1953), 105–115.

    Google Scholar 

  5. Loomis, L. H., & D. V. Widder, The Poisson integral representation of functions which are positive and harmonic in a half-plane. Duke Math. J. 9, 643–645 (1942).

    Google Scholar 

  6. Rosenbloom, P. C., & D. V. Widder, A temperature function which vanishes initially. Amer. Math. Monthly 65, 607–609 (1958).

    Google Scholar 

  7. Rosenbloom, P. C., & D. V. Widder, Expansions in terms of heat polynomials and associated functions. Trans. Amer. Math. Soc. 92, 220–266 (1959).

    Google Scholar 

  8. Widder, D. V., The Laplace Transform. Princeton: Univ Press 1941.

    Google Scholar 

  9. Widder, D. V., Positive temperatures on an infinite rod. Trans. Amer. Math. Soc. 55, 85–95 (1944).

    Google Scholar 

  10. Widder, D. V., Series expansions of solutions of the heat equation in n dimensions. Annali di Mat. Pura e Appl. 55, 389–410 (1961).

    Google Scholar 

  11. Widder, D. V., Analytic solutions of the heat equation. Duke Math. J. 29, 497–504 (1962).

    Google Scholar 

  12. Widder, D. V., Functions of three variables which satisfy both the heat equation and Laplace's equation in two variables. J. Australian Math. Soc. 3, 396–407 (1963).

    Google Scholar 

  13. Widder, D. V., The rôle of the Appell transformation in the theory of heat conduction. Trans. Amer. Math. Soc. 109, 121–134 (1963).

    Google Scholar 

  14. Widder, D. V., A problem of Kampé de Fériet. J. of Math. Anal. and Appl. 9, 458–468 (1964).

    Google Scholar 

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Authors and Affiliations

  1. Harvard University, Cambridge, Massachusetts

    D. V. Widder

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  1. D. V. Widder
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Communicated by A. Erdélyi

This research was supported in part by the United States Air Force Office of Scientific Research, under Contract AFSOR 393-63.

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Widder, D.V. Some analogies from classical analysis in the theory of heat conduction. Arch. Rational Mech. Anal. 21, 108–119 (1966). https://doi.org/10.1007/BF00266570

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