Abstract.
In our previous works we have constructed operator equalities which transform scalar singular integral operators with shift to matrix characteristic singular integral operators without shift and found some of their applications to problems with shift. In this article the operator equalities are used for the study of matrix characteristic singular integral operators.
Conditions for the invertibility of the singular integral operators with orientation preserving shift and coefficients with a special structure generated by piecewise constant functions, t, t −1, were found.
Conditions for the invertibility of the matrix characteristic singular integral operators with four-valued piecewise constant coefficients of a special structure were likewise obtained.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Submitted: June 15, 2007. Revised: October 25, 2007. Accepted: November 5, 2007.
Rights and permissions
About this article
Cite this article
Karelin, A. Singular Integral Operators with Coefficients of a Special Structure Related to Operator Equalities. Complex anal.oper. theory 2, 549–567 (2008). https://doi.org/10.1007/s11785-008-0066-x
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11785-008-0066-x