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Microlocal analysis of quasianalytic Gelfand-Shilov type ultradistributions |
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| Authors: | Marco Cappiello René Schulz |
| Affiliation: | 1. Department of Mathematics, University of Torino, Via Carlo Alberto 10, 10123Torino, Italy.marco.cappiello@unito.it;3. Institut für Analysis, Leibniz Universit?t Hannover, Welfenplatz 1, D–30167Hannover, Germany. |
| Abstract: | We introduce a global wave front set suitable for the analysis of tempered ultradistributions of quasi-analytic Gelfand–Shilov type. We study the transformation properties of the wave front set and use them to give microlocal existence results for pullbacks and products. We further study quasi-analytic microlocality for classes of localization and ultradifferential operators, and prove microellipticity for differential operators with polynomial coefficients. |
| Keywords: | Gelfand–Shilov spaces global wave front sets Bargmann transform localization operators tempered ultradistributions |