Abstract
We study the algebra A generated by singular integral operators a I+b S and the operator of complex conjugation V on the weighted Lebesgue space L p(Γ,w). Our approach is based on transforming the operators in A locally into Mellin pseudodifferential operators. By having recourse to the Fredholm and index theory of the latter class of operators, we can establish Fredholm criteria and index formulas for operators in A with slowly oscillating coefficients in the case of slowly oscillating composed curves F and slowly oscillating Muckenhoupt weights w. We are in particular able to consider curves with whirl points, in which case massive local spectra may emerge even for constant coefficients and weights.
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Böttcher, A., Karlovich, Y.I., Rabinovich, V.S. (2001). Singular integral operators with complex conjugation from the viewpoint of pseudodifferential operators. In: Elschner, J., Gohberg, I., Silbermann, B. (eds) Problems and Methods in Mathematical Physics. Operator Theory: Advances and Applications, vol 121. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8276-7_5
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DOI: https://doi.org/10.1007/978-3-0348-8276-7_5
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