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http://hdl.handle.net/10071/10066
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Title: Fredholmness of Toeplitz operators and corona problems
Authors: Câmara, M. C.
Diogo, C.
Rodman, L.
Keywords: Corona theorem
Riemann-Hilbert problem
Toeplitz operator
Wiener-Hopf factorization
Issue Date: 2010
Publisher: Elsevier Science
Abstract: A meromorphic analogue to the corona problem is formulated and studied and its solutions are characterized as being left-invertible in a space of meromorphic functions. The Fredholmness of Toeplitz operators with symbol G ∈ (L∞(R))2×2 is shown to be equivalent to that of a Toeplitz operator with scalar symbol γ:=det G, provided that the Riemann-Hilbert problem G φM+ = φ M- admits a solution such that the meromorphic corona problems with data φM± are solvable. The Fredholm properties are characterized in terms of φM± and the corresponding meromorphic left-inverses. Partial index estimates for the symbols and Fredholmness criteria are established for several classes of Toeplitz operators.
Description: WOS:000278700900008 (Nº de Acesso Web of Science)
Peer reviewed: Sim
URI: https://ciencia.iscte-iul.pt/public/pub/id/22846
http://hdl.handle.net/10071/10066
ISSN: 0022-1236
Publisher version: The definitive version is available at: http://dx.doi.org/10.1016/j.jfa.2010.04.013
Appears in Collections:DM-RI - Artigos em revistas científicas internacionais

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