# IJPAM: Volume 64, No. 1 (2010)

ON THE OPERATOR RELATED TO
THE BESSEL HEAT EQUATION

Somboon Niyom, Amnuay Kananthai
Department of Mathematics
Faculty of Science
Chiang Mai University
Chiang Mai, 50200, THAILAND
e-mail: [email protected]
e-mail: [email protected]

Abstract.In this paper, we study the equation

with the initial condition for , where the operator is defined by

is the dimension of the space , , , , , is an unknown function for , is a generalized function, is a positive integer and is a positive constant. We obtain the solution of such equation which is related to the spectrum and the heat kernel. Moreover, such Bessel heat kernel has interesting properties and also related to the kernel of an extension of the heat equation.