Sharp heat kernel estimates in the Fourier-Bessel setting for a   continuous range of the type parameter
  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. 
Adam Nowak, Luz Roncal
math.CA