Abstract
Let , where is the unit circle, and let be the Hilbert space of vector-valued functions whose components are complex-valued square integrable functions on . The author considers the subspace of functions in having analytic continuations into the torus ; let be the projection of onto . For a bounded measurable matrix-valued function of order on having limits and ( uniform in , the bounded operator is defined in . In this paper a homotopy method is described for computing the index of Noetherian operators in the -algebra generated by the operators . In the case where is continuous a simple formula for computing the index of is indicated.Bibliography: 24 titles.
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