Document Zbl 1200.47065

Cordero, Elena; Pilipović, Stevan; Rodino, Luigi; Teofanov, Nenad

Quasianalytic Gelfand-Shilov spaces with application to localization operators. (English) Zbl 1200.47065

Rocky Mt. J. Math. 40, No. 4, 1123-1147 (2010).

Using the heat kernel and parametrix techniques, the authors give a new structure theorem for those distributions in the dual of projective (respectively, inductive) limits of quasianalytic Gelfand-Shilov spaces of type \(S\) which can be extended to ultradistributions of Beurling (respectively, Roumieu) type. They prove that such quasianalytic ultradistributions, taken as symbols, produce trace-class localization operators. To this end, they study time-frequency representations on the primal spaces, which are shown to be projective (respectively, inductive) limits of modulation spaces with weights of exponential growth.

Reviewer: Isabel Marrero (La Laguna)

Cited in 37 Documents

MSC:

47G30	Pseudodifferential operators
35S05	Pseudodifferential operators as generalizations of partial differential operators
46F05	Topological linear spaces of test functions, distributions and ultradistributions
44A05	General integral transforms

Keywords:

localization operator; quasianalytic ultradistribution; Gelfand-Shilov space; modulation space; Wigner distribution; short-time Fourier transform; trace-class operator

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References:

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