Singular Integral Operators with Coefficients of a Special Structure Related to Operator Equalities |
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Authors: | Aleksandr Karelin |
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Institution: | (1) Universidad Autonoma del Estado de Hidalgo ICBI CIAII, Carretera Pachuca-Tulancingo km.4.5, C.P. 42184 Pachuca, Hidalgo, Mexico |
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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.
Submitted: June 15, 2007. Revised: October 25, 2007. Accepted: November 5, 2007. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) Primary 47G10 45E99 54F15 |
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