We consider the spaces of ultradifferentiable functions $S_omega$ as introduced by Björck (and its dual $S'_omega$) and we use time-frequency analysis to define a suitable wave front set in this setting and obtain several applications: global regularity properties of pseudodifferential operators of infinite order and the micro-pseudolocal behaviour of partial differential operators with polynomial coefficients and of localization operators with symbols of exponential growth. Moreover, we prove that the new wave front set, defined in terms of the Gabor transform, can be described using only Gabor frames. Finally, some examples show the convenience of the use of weight functions to describe more precisely the global regularity of (ultra)distributions.

The Gabor wave front set in spaces of ultradifferentiable functions

BOITI, Chiara;Alessandro Oliaro
2019

Abstract

We consider the spaces of ultradifferentiable functions $S_omega$ as introduced by Björck (and its dual $S'_omega$) and we use time-frequency analysis to define a suitable wave front set in this setting and obtain several applications: global regularity properties of pseudodifferential operators of infinite order and the micro-pseudolocal behaviour of partial differential operators with polynomial coefficients and of localization operators with symbols of exponential growth. Moreover, we prove that the new wave front set, defined in terms of the Gabor transform, can be described using only Gabor frames. Finally, some examples show the convenience of the use of weight functions to describe more precisely the global regularity of (ultra)distributions.
2019
Boiti, Chiara; David, Jornet; Oliaro, Alessandro
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/2372232
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