Asymptotic behaviour of the Bessel heat kernels

Abstract

We consider Dirichlet heat kernel p_a^{(mu )}(t,x,y) for the Bessel differential operator L^{(mu )}=frac{d^2}{dx^2}+frac{2mu +1}{2x}, mu in mathbf {R}, in half-line (a,infty ), a>0, and provide its asymptotic expansions for xy/trightarrow infty .