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Title: Invertibility of Toeplitz operators and corona conditions in a strip
Authors: Câmara, M. C.
Diogo, C.
Keywords: Toeplitz operator
Riemann–Hilbert problem
Corona theorem
Wiener–Hopf factorization
Issue Date: 2008
Publisher: Academic Press/Elsevier
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.
Description: WOS:000254945300042
Peer reviewed: yes
DOI: 10.1016/j.jmaa.2007.12.059
ISSN: 0022-247X
Appears in Collections:DM-RI - Artigos em revistas científicas internacionais

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