Microlocal analysis of quasianalytic Gelfand-Shilov type ultradistributions. (English) Zbl 1339.35014
Summary: 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.
MSC:
| 35A27 | Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs |
| 35A18 | Wave front sets in context of PDEs |
| 35A22 | Transform methods (e.g., integral transforms) applied to PDEs |
| 46F05 | Topological linear spaces of test functions, distributions and ultradistributions |
Keywords:
Gelfand-Shilov spaces; global wave front sets; Bargmann transform; localization operators; tempered ultradistributionsReferences:
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