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Some properties of the kernel and the cokernel of Toeplitz operators with matrix symbols. (English) Zbl 1183.47021

The relation between kernels and cokernels of Toeplitz operators are studied in connection with certain relations between their symbols by the use of a Riemann-Hilbert approach. This approach is even applicable if the symbol possesses no factorization and has the advantage that simple linear algebraic and complex analytic techniques can be used. The obtained results are applied to Toeplitz operators in \((H_2^*)^2\) which have the property that the determinant of the symbol admits a bounded Wiener-Hopf factorization.

MSC:

47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
35Q15 Riemann-Hilbert problems in context of PDEs
47A68 Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators
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References:

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