We study localization operators with symbols in spaces of quasi-analytic distributions. More precisely, it is shown that certain quasianalytic distributions, considered as symbols, give rise to trace-class localization operators. We give a new structure theorem for quasianalytic distributions which combines its local and global properties. In the proof we use the heat kernel and parametrix techniques, while in the study of localization operators we use the techniques of time-frequency analysis.
Quasianalytic Gelfand-Shilov spaces and localization operators
CORDERO, Elena;RODINO, Luigi Giacomo;
2010-01-01
Abstract
We study localization operators with symbols in spaces of quasi-analytic distributions. More precisely, it is shown that certain quasianalytic distributions, considered as symbols, give rise to trace-class localization operators. We give a new structure theorem for quasianalytic distributions which combines its local and global properties. In the proof we use the heat kernel and parametrix techniques, while in the study of localization operators we use the techniques of time-frequency analysis.
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