Abstract
We study the local Fredholm spectra and global Fredholm properties for singular integral operators on composed Carleson curves with discontinuous coefficients acting on weighted Holder spaces. We consider the curves, coefficients, and weights which are slowly oscillating at the nodes of the curve. Application of pseudodifferential operators technique allows us to explain the influence of oscillation of curves, coefficients, and weights on the appearance of massive local Fredholm spectra. We obtain a criterion of Fredholmness and index formula for operators under consideration.
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