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

Full-text PDF Free Access

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.**37**(1970), 57-62. MR**0271652 (42:6535)****[2]**F. M. Cholewinski and D. T. Haimo,*The Weierstrass-Hankel convolution transform*, J. Analyse Math.**17**(1966), 1-58. MR**35**#5866. MR**0215021 (35:5866)****[3]**-,*Integral representations of solutions of the generalized heat equation*, Illinois J. Math.**10**(1966), 623-638. MR**33**#7796. MR**0199653 (33:7796)****[4]**D. T. Haimo,*Expansions in terms of generalized heat polynomials and of their Appell transforms*, J. Math. Mech.**15**(1966), 735-758. MR**33**#4340. MR**0196148 (33:4340)****[5]**-,*Generalized temperature functions*, Duke Math. J.**33**(1966), 305-322. MR**34**#1802. MR**0201924 (34:1802)****[6]**-,*Series representation of generalized temperature functions*, SIAM J. Appl. Math.**15**(1967), 359-367. MR**35**#3204. MR**0212331 (35:3204)****[7]**-,*Equivalence of integral transform and series expansion representation of generalized temperatures*, Analytic Methods in Mathematical Physics, Gordon and Breach, New York, 1970, pp. 453-459. MR**0361639 (50:14084)****[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**28**#4140. MR**0160931 (28:4140)****[9]**-,*A problem of Kampé de Fériet*, J. Math. Anal. Appl.**9**(1964), 458-467. MR**34**#8107. MR**0208297 (34:8107)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
35.78

Retrieve articles in all journals with MSC: 35.78

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