Generalized Gaussian bounds for discrete convolution powers

• Jean-François Coulombel ^[1] ; Grégory Faye ^[1]
  1. [1] Université de Toulouse

     Université de Toulouse

     Arrondissement de Toulouse, Francia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 5, 2022, págs. 1553-1604
• Idioma: inglés
• DOI: 10.4171/RMI/1338
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• Resumen

  • 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