An integral representation for generalized temperatures in two space variables

Author:
Deborah Tepper Haimo

Journal:
Proc. Amer. Math. Soc. **30** (1971), 533-538

MSC:
Primary 35.78

DOI:
https://doi.org/10.1090/S0002-9939-1971-0283421-1

MathSciNet review:
0283421

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Abstract | References | Similar Articles | Additional Information

Abstract: An integral representation is derived for a function which satisfies the generalized heat equation in one of the space variables and the adjoint generalized heat equation in the other space variable.

**[1]**F. M. Cholewinski, D. T. Haimo, and A. E. Nussbaum,*A necessary and sufficient condition for the representation of a function as a Hankel-Stieltjes transform*, Studia Math.**36**(1970), 269–274. MR**0271652**, https://doi.org/10.4064/sm-36-3-269-274**[2]**Frank M. Cholewinski and Deborah Tepper Haimo,*The Weierstrass-Hankel convolution transform*, J. Analyse Math.**17**(1966), 1–58. MR**0215021**, https://doi.org/10.1007/BF02788651**[3]**Deborah Tepper Haimo and Frank M. Cholewinski,*Integral representations of solutions of te generalized heat equation*, Illinois J. Math.**10**(1966), 623–638. MR**0199653****[4]**Deborah Tepper Haimo,*Expansions in terms of generalized heat polynomials and of their Appell transforms*, J. Math. Mech.**15**(1966), 735–758. MR**0196148****[5]**Deborah Tepper Haimo,*Generalized temperature functions*, Duke Math. J.**33**(1966), 305–322. MR**0201924****[6]**Deborah Tepper Haimo,*Series representation of generalized temperature functions*, SIAM J. Appl. Math.**15**(1967), 359–367. MR**0212331**, https://doi.org/10.1137/0115033**[7]**Deborah Tepper Haimo,*Equivalence of integral transform and series expansion representations of generalized temperatures*, Analytic methods in mathematical physics (Sympos., Indiana Univ., Bloomington, Ind., 1968) Gordon and Breach, New York, 1970, pp. 453–459. MR**0361639****[8]**D. V. Widder,*Functions of three variables which satisfy both the heat equation and Laplace’s equation in two variables*, J. Austral. Math. Soc.**3**(1963), 396–407. MR**0160931****[9]**D. V. Widder,*A problem of Kampé de Fériet*, J. Math. Anal. Appl.**9**(1964), 458–467. MR**0208297**, https://doi.org/10.1016/0022-247X(64)90029-0

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1971-0283421-1

Keywords:
Generalized temperatures,
integral representations,
generalized heat equation,
Bessel function

Article copyright:
© Copyright 1971
American Mathematical Society