| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Coimbra, Dept Math, CMUC, Coimbra - Portugal
[2] Austrian Acad Sci, Acoust Res Inst, A-1040 Vienna - Austria
Total Affiliations: 2
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| 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 Opportunities: | Scholarships in Brazil - Post-Doctoral |