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|Title:||Invertibility of Toeplitz operators and corona conditions in a strip|
|Authors:||Câmara, M. C.|
|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.|
|Appears in Collections:||DM-RI - Artigos em revistas científicas internacionais|
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|Diogo 2008 J Math Anal Appl 342(2)129.pdf||228.18 kB||Adobe PDF||View/Open Request a copy|
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