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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)


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Abreu, Luis Daniel [1, 2] ; Faustino, Nelson [1]
Total Authors: 2
[1] Univ Coimbra, Dept Math, CMUC, Coimbra - Portugal
[2] Austrian Acad Sci, Acoust Res Inst, A-1040 Vienna - Austria
Total Affiliations: 2
Document type: Journal article
Source: Proceedings of the American Mathematical Society; v. 143, n. 10, p. 4317-4323, OCT 2015.
Web of Science Citations: 1

This note is a contribution to a problem of Lewis Coburn concerning the relation between Toeplitz operators and Gabor-Daubechies localization operators. We will show that, for any localization operator with a general window w is an element of F-2(C) (the Fock space of analytic functions square-integrable on the complex plane), there exists a differential operator of infinite order D, with constant coefficients explicitly determined by w, such that the localization operator with symbol f coincides with the Toeplitz operator with symbol Df. This extends results of Coburn, Lo and Englis, who obtained similar results in the case where w is a polynomial window. Our technique of proof combines their methods with a direct sum decomposition in true polyanalytic Fock spaces. Thus, polyanalytic functions are used as a tool to prove a theorem about analytic functions. (AU)

FAPESP's process: 13/07590-8 - Applications of discrete Clifford calculus in field theories
Grantee:Nelson José Rodrigues Faustino
Support type: Scholarships in Brazil - Post-Doctorate