Almost periodic pseudodifferential operators and Gevrey classes

2011/02/22 by Alessandro Oliaro, Oliaro, Alessandro, Luigi Rodino +3
Mathematics · #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math.AP #math.FA #msc:35B15 #msc:35B65 #msc:35H10 #msc:35S05

paper · pdf · doi:10.48550/arxiv.1102.4553

40 pages

arxiv created 2011/02/22 · arxiv updated 2011/02/23

Abstract

We study almost periodic pseudodifferential operators acting on almost periodic functions G_{\rm ap}^s(\rr d) of Gevrey regularity index s ≥ 1. We prove that almost periodic operators with symbols of Hörmander type S_ρ,δ^m satisfying an s-Gevrey condition are continuous on G_{\rm ap}^s(\rr 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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