Almost periodic pseudodifferential operators and Gevrey classes |
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Authors: | Alessandro Oliaro Luigi Rodino Patrik Wahlberg |
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Affiliation: | 1. Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123, Torino (TO), Italy
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Abstract: | We study almost periodic pseudodifferential operators acting on almost periodic functions ${G_{rm ap}^s(mathbb {R}^d)}$ of Gevrey regularity index s ≥ 1. We prove that almost periodic operators with symbols of H?rmander type ${S_{rho,delta}^m}$ satisfying an s-Gevrey condition are continuous on ${G_{rm ap}^s(mathbb {R}^d)}$ provided 0 < ρ ≤ 1, δ?=?0 and s ρ ≥ 1. A calculus is developed for symbols and operators using a notion of regularizing operator adapted to almost periodic Gevrey functions and its duality. We apply the results to show a regularity result in this context for a class of hypoelliptic operators. |
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