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http://hdl.handle.net/10071/10066| Author(s): | Câmara, M. C. Diogo, C. Rodman, L. |
| Date: | 2010 |
| Title: | Fredholmness of Toeplitz operators and corona problems |
| Volume: | 259 |
| Number: | 5 |
| Pages: | 1273-1299 |
| ISSN: | 0022-1236 |
| Keywords: | Corona theorem Riemann-Hilbert problem Toeplitz operator Wiener-Hopf factorization |
| 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. |
| Peerreviewed: | Sim |
| Access type: | Embargoed Access |
| Appears in Collections: | DM-RI - Artigos em revistas científicas internacionais com arbitragem científica |
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|---|---|---|---|---|
| publisher_version_J_Functional_Analysis.pdf Restricted Access | 257,11 kB | Adobe PDF | View/Open Request a copy |
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