Centre for Mathematics, University of Coimbra

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Type:	Preprint
National /International:	International
Title:	On Toeplitz operators and localization operators
Publication Date:	2013-08-09
Authors:	- Luís Daniel Abreu - Nelson Faustino
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 \in F₂(C) (the Fock space of analytic functions square-integrable on the complex plane), there exists a dierential operator of innite 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.
Institution:	DMUC 13-34
Online version:	http://www.mat.uc.pt...prints/eng_2013.html
Download:	Not available