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Vector semi-Fredholm Toeplitz operators and mean winding numbers

Dmitry V. Yakubovich
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Abstract

For a continuous complex-valued function g on the real line without zeros, several notions of a mean winding number are introduced. We give necessary conditions for a Toeplitz operator with matrix-valued symbol G to be semi-Fredholm in terms of mean winding numbers of det G. The matrix function G is assumed to be continuous on the real line, and no other apriori assumptions on it are made.

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Dmitry V. Yakubovich. 2008-12-22. Vector semi-Fredholm Toeplitz operators and mean winding numbers. https://arxiv.org/abs/math/0606153

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