Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand
Copyright © 2010 Wanchak Satsanit. This is an open access article distributed under the
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We study the equation with the initial condition for The operator is the operator iterated k-times and is defined by , where is the dimension of the , , , , , and is a nonnegative integer, is an unknown function for , is a given generalized function, and is a positive constant. We obtain the solution of such equation, which is related to the spectrum and the kernel, which is so called Bessel heat kernel. Moreover, such Bessel heat kernel has interesting properties and also related to the kernel of an extension of the heat equation.