Asymptotic behaviour of the Bessel heat kernels

Abstract

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

19 pages