Pseudo‐differential operators in a Gelfand–Shilov setting

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. Moreover, we deduce composition and certain invariance properties of these classes.

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Bibliographic Details
Published in:Mathematische Nachrichten 2017-04, Vol.290 (5-6), p.738-755
Main Authors: Cappiello, Marco, Toft, Joachim
Format: Article
Language:English
Subjects:
35S05
46F05
Gelfand–Shilov spaces
Matematik
Mathematics
modulation spaces
Pseudo-differential operators
short-time Fourier transform
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Description
Summary: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. Moreover, we deduce composition and certain invariance properties of these classes.
ISSN:0025-584X
1522-2616
1522-2616
DOI:10.1002/mana.201500465