ON TOEPLITZ OPERATORS AND LOCALIZATION OPERATORS

Autor(es)

Abreu, Luis Daniel ^{[1, 2]} ; Faustino, Nelson ^[1]

Afiliação do(s) autor(es)

^[1] Univ Coimbra, Dept Math, CMUC, Coimbra - Portugal

^[2] Austrian Acad Sci, Acoust Res Inst, A-1040 Vienna - Austria

• Tipo de documento: Artigo Científico
• Fonte: Proceedings of the American Mathematical Society; v. 143, n. 10, p. 4317-4323, OCT 2015.
• Citações Web of Science: 1

Resumo

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)

• Processo FAPESP: 13/07590-8 - Aplicações de Cálculo de Clifford discreto em teorias de campos quânticos
• Beneficiário: Nelson José Rodrigues Faustino
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado