Generalized gaussian bounds for discrete convolution powers
Numerical Analysis
2021-11-23 v2 Numerical Analysis
Probability
Abstract
We prove a uniform generalized gaussian bound for the powers of a discrete convolution operator in one space dimension. Our bound is derived under the assumption that the Fourier transform of the coefficients of the convolution operator is a trigonometric rational function, which generalizes previous results that were restricted to trigonometric polynomials. We also allow the modulus of the Fourier transform to attain its maximum at finitely many points over a period.
Cite
@article{arxiv.2012.09437,
title = {Generalized gaussian bounds for discrete convolution powers},
author = {Jean-François Coulombel and Grégory Faye},
journal= {arXiv preprint arXiv:2012.09437},
year = {2021}
}