Polynomial Analogue Research Articles

Previous article Next article Series Representation of Generalized Temperature FunctionsDeborah Tepper HaimoDeborah Tepper Haimohttps://doi.org/10.1137/0115033PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] L. R. Bragg, The radial heat polynomials and related functions, Trans. Amer. Math. Soc., 119 (1965), 270–290 MR0181769 0141.29201 CrossrefISIGoogle Scholar[2] H. S. Carslaw and , J. C. Jaeger, Conduction of heat in solids, Oxford University Press, Oxford, 1959 0095.30201 Google Scholar[3] Frank M. Cholewinski and , Deborah Tepper Haimo, The Weierstrass-Hankel convolution transform, J. Analyse Math., 17 (1966), 1–58 MR0215021 0171.09902 CrossrefISIGoogle Scholar[4] Deborah Tepper Haimo, Generalized temperature functions, Duke Math. J., 33 (1966), 305–322 10.1215/S0012-7094-66-03335-7 MR0201924 0144.14202 CrossrefISIGoogle Scholar[5] Deborah Tepper Haimo, Functions with the Huygens property, Bull. Amer. Math. Soc., 71 (1965), 528–532 MR0178313 0149.07004 CrossrefISIGoogle Scholar[6] Deborah Tepper Haimo, Expansions in terms of generalized heat polynomials and of their Appell transforms, J. Math. Mech., 15 (1966), 735–758 MR0196148 ISIGoogle Scholar[7] Deborah Tepper Haimo, $L\sp{2}$ expansions in terms of generalized heat polynomials and of their Appell transforms, Pacific J. Math., 15 (1965), 865–875 MR0185383 0138.35302 CrossrefISIGoogle Scholar[8] Deborah Tepper Haimo, Series expansions of generalized temperature functions in N dimensions, Canad. J. Math., 18 (1966), 794–802 MR0201925 0144.35503 CrossrefISIGoogle Scholar[9] P. C. Rosenbloom and , D. V. Widder, Expansions in terms of heat polynomials and associated functions, Trans. Amer. Math. Soc., 92 (1959), 220–266 MR0107118 0086.27203 CrossrefGoogle Scholar[10] D. V. Widder, Analytic solutions of the heat equation, Duke Math. J., 29 (1962), 497–503 10.1215/S0012-7094-62-02950-2 MR0157127 0109.04604 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Numerical approximation of the one-dimensional inverse Cauchy–Stefan problem using heat polynomials methodsComputational and Applied Mathematics, Vol. 41, No. 4 | 28 May 2022 Cross Ref A heat polynomial method for inverse cylindrical one-phase Stefan problemsInverse Problems in Science and Engineering, Vol. 29, No. 13 | 16 November 2021 Cross Ref Polynomial solutions to Cauchy problems for complex Bessel operatorsComplex Variables, Theory and Application: An International Journal, Vol. 50, No. 7-11 | 30 August 2006 Cross Ref Heat polynomial analogues for equations with higher order time derivativesJournal of Mathematical Analysis and Applications, Vol. 295, No. 2 | 1 Jul 2004 Cross Ref A numerical method for semilinear singular parabolic quenching problemsQuarterly of Applied Mathematics, Vol. 47, No. 1 | 1 January 1989 Cross Ref Polynomial Expansions for Solutions of the System $D_{X_1}^k U(X_1 , \cdots ,X_r ) = D_{X_k} U(X_1 , \cdots ,X_r )^ * $Hans KemnitzSIAM Journal on Mathematical Analysis, Vol. 16, No. 2 | 17 July 2006AbstractPDF (864 KB)Generalized axially symmetric heat potentials and singular parabolic initial boundary value problemsArchive for Rational Mechanics and Analysis, Vol. 79, No. 4 | 1 Dec 1982 Cross Ref Polynomial Expansions for Solutions of $D_x^r u(x,t) = D_t u(x,t),r = 2,3,4, \cdots $Hans KemnitzSIAM Journal on Mathematical Analysis, Vol. 13, No. 4 | 17 July 2006AbstractPDF (746 KB)Zum Cauchy-Problem bei der verallgemeinerten W�rmeleitungsgleichungMonatshefte f�r Mathematik, Vol. 81, No. 3 | 1 Sep 1976 Cross Ref On a singular parabolic equation related to axially symmetric heat potentialsAnnali di Matematica Pura ed Applicata, Vol. 105, No. 1 | 1 Dec 1975 Cross Ref BibliographyPure and Applied Mathematics | 1 Jan 1975 Cross Ref An integral representation for generalized temperatures in two space variablesProceedings of the American Mathematical Society, Vol. 30, No. 3 | 1 January 1971 Cross Ref Cauchy's problem for a singular parabolic partial differential equationJournal of Differential Equations, Vol. 8, No. 2 | 1 Sep 1970 Cross Ref Classical Analysis and the Generalized Heat EquationFrank M. Cholewinski and Deborah Tepper HaimoSIAM Review, Vol. 10, No. 1 | 18 July 2006AbstractPDF (941 KB) Volume 15, Issue 2| 1967SIAM Journal on Applied Mathematics231-477 History Submitted:30 March 1966Published online:13 July 2006 InformationCopyright © 1967 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0115033Article page range:pp. 359-367ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics

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