In the paper we consider the Bessel differential operator L^(\mu)=\dfrac{ d^2}{ dx^2}+\dfrac{ 2\mu+1}{ x}\dfrac{ d}{ dx} in half-line (a,\infty), a>0, and its Dirichlet heat kernel p_a^(\mu)(t,x,y). For \mu=0, by combining analytical and probabilistic methods, we provide sharp two-sided estimates of the heat kernel for the whole range of the space parameters x,y>a and every t>0, which complements the recent results given in [1], where the case \mu\neq 0 was considered.
Categories: math.AP math.PR