A Gaussian bound for convolutions of functions on locally compact groups
Volume 176 / 2006
Studia Mathematica 176 (2006), 201-213
MSC: 60B15, 60G50, 22E30.
DOI: 10.4064/sm176-3-2
Abstract
We give new and general sufficient conditions for a Gaussian upper bound on the convolutions $K_{m+n} * K_{m+n-1} * \cdots * K_{m+1}$ of a suitable sequence $K_1, K_2, K_3, \ldots$ of complex-valued functions on a unimodular, compactly generated locally compact group. As applications, we obtain Gaussian bounds for convolutions of suitable probability densities, and for convolutions of small perturbations of densities.
