Abstract
The generalized heat equation is given by1.1where Δxf(x) = f″(x) + (2v/x)f′(x), v a fixed positive number. In a recent paper (5), the author established criteria for representing solutions of (1.1) in either the form1.2or1.3where Pn,v(x, t) is t he polynomial solution of (1.1) given explicitly by1.4and Wn,v(x, t) is its Appell transform; cf. (1). Our object is to generalize these results by extending them to higher dimensions. D. V. Widder (8) studied the problem for the ordinary heat equation.
Publisher
Canadian Mathematical Society
Cited by
8 articles.
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1. Polynomial solutions to Cauchy problems for complex Bessel operators;Complex Variables, Theory and Application: An International Journal;2005-06-10
2. Heat polynomial analogues for equations with higher order time derivatives;Journal of Mathematical Analysis and Applications;2004-07
3. 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 )^ * $;SIAM Journal on Mathematical Analysis;1985-03
4. Polynomial Expansions for Solutions of $D_x^r u(x,t) = D_t u(x,t),r = 2,3,4, \cdots $;SIAM Journal on Mathematical Analysis;1982-07
5. Expansions in terms of Laguerre heat polynomials and of their temperature transforms;Journal d'Analyse Mathématique;1971-12