Please use this identifier to cite or link to this item:
http://hdl.handle.net/10071/5622
Author(s): | Câmara, M. C. Diogo, C. |
Date: | 2008 |
Title: | Invertibility of Toeplitz operators and corona conditions in a strip |
Volume: | 342 |
Number: | 2 |
Pages: | 1297 - 1317 |
Reference: | Câmara, M. C., & Diogo, C. (2008). Invertibility of Toeplitz operators and corona conditions in a strip. Journal of Mathematical Analysis and Applications, 342(2), 1297-1317. https://10.1016/j.jmaa.2007.12.059 |
ISSN: | 0022-247X |
DOI (Digital Object Identifier): | 10.1016/j.jmaa.2007.12.059 |
Keywords: | Toeplitz operator Riemann–Hilbert problem Corona theorem Wiener–Hopf factorization |
Abstract: | A Toeplitz operator with symbol G such that detG=1 is invertible if there is a non-trivial solution to a Riemann–Hilbert problem G?+=?? with ?+ and ?? satisfying the corona conditions in C+ and C?, respectively. However, determining such a solution and verifying that the corona conditions are satisfied are in general difficult problems. In this paper, on one hand, we establish conditions on ?± which are equivalent to the corona conditions but easier to verify, if G±1 are analytic and bounded in a strip. This happens in particular with almost-periodic symbols. On the other hand, we identify new classes of symbols G for which a non-trivial solution to G?+=?? can be explicitly determined and the corona conditions can be verified by the above mentioned approach, thus obtaining invertibility criteria for the associated Toeplitz operators. |
Peerreviewed: | yes |
Access type: | Restricted Access |
Appears in Collections: | DM-RI - Artigos em revistas científicas internacionais com arbitragem científica |
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