Advanced search
Start date
Betweenand
Related content
(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

ON TOEPLITZ OPERATORS AND LOCALIZATION OPERATORS

Full text
Author(s):
Abreu, Luis Daniel [1, 2] ; Faustino, Nelson [1]
Total Authors: 2
Affiliation:
[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
Abstract

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