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.

翻译：我们证明,我们是一个统一的通用的百日咳,在一个空间层面被一个离散的革命操作员的权力所约束,我们的义务来自这样一种假设,即富里叶革命操作员系数的变换是一个三角性理性功能,它概括了以前仅限于三角性多元分子的结果。 我们还允许富里叶变换的模范在一段时间内达到其极限,在有限的多个点上达到其极限。