Sharp heat kernel estimates in the Fourier-Bessel setting for a continuous range of the type parameter

Abstract

The heat kernel in the setting of classical Fourier-Bessel expansions is defined by an oscillatory series which cannot be computed explicitly. We prove qualitatively sharp estimates of this kernel. Our method relies on establishing a connection with a situation of expansions based on Jacobi polynomials and then transferring known sharp bounds for the related Jacobi heat kernel.

8 pages; v2 (now all possible parameters of type admitted)

Cited by in corpus (1)

• Hardy spaces for Fourier--Bessel expansions