We study an anisotropic version of the Shubin calculus of pseudodifferential operators on R-d Anisotropic symbols and Gabor wave front sets are defined in terms of decay or growth along curves in phase space of power type parametrized by one positive parameter that distinguishes space and frequency variables. We show that this gives subcalculi of Shubin's isotropic calculus, and we show a microlocal as well as a microelliptic inclusion in the framework. Finally we prove an inclusion for the anisotropic Gabor wave front set of chirp type oscillatory functions with a real polynomial phase function.

Anisotropic global microlocal analysis for tempered distributions / Rodino, L.; Wahlberg, P.. - In: MONATSHEFTE FÜR MATHEMATIK. - ISSN 0026-9255. - (2022). [10.1007/s00605-022-01812-z]

Anisotropic global microlocal analysis for tempered distributions

Wahlberg P.
2022

Abstract

We study an anisotropic version of the Shubin calculus of pseudodifferential operators on R-d Anisotropic symbols and Gabor wave front sets are defined in terms of decay or growth along curves in phase space of power type parametrized by one positive parameter that distinguishes space and frequency variables. We show that this gives subcalculi of Shubin's isotropic calculus, and we show a microlocal as well as a microelliptic inclusion in the framework. Finally we prove an inclusion for the anisotropic Gabor wave front set of chirp type oscillatory functions with a real polynomial phase function.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2974734