Generalized Gaussian bounds for discrete convolution powers
Résumé
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.
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