Pseudo-differential operators in a Gelfand-Shilov setting

2015/05/15 by Marco Cappiello, Cappiello, Marco, Joachim Toft +1
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.1505.04096

22 pages. Some details are updated compared to earlier versions

arxiv created 2016/01/20 · arxiv updated 2016/01/21

Abstract

We introduce some general classes of pseudodifferential operators with symbols admitting exponential type growth at infinity and we prove mapping properties for these operators on Gelfand-Shilov spaces both in the quasi-analytic and in the non-quasi-analytic case. Moreover, we prove composition theorems and certain invariance properties of these classes.

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