Fredholmness of Toeplitz operators and corona problems
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 sca...
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| Other Authors: | , |
| Format: | article |
| Language: | eng |
| Published: |
2015
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| Subjects: | |
| Online Access: | https://ciencia.iscte-iul.pt/public/pub/id/22846 |
| Country: | Portugal |
| Oai: | oai:repositorio.iscte-iul.pt:10071/10066 |
| Summary: | 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. |
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