Abstract:
Singular integral operators of two types are considered on a piecewise smooth contour in weighted Lebesgue spaces with generalized Cauchy kernels, related to the parametrix of elliptic systems of first order on the plane. The operators of the first type are linear over the field of complex numbers and are represented as a usual combination of the generalized singular Cauchy operator and the operators of multiplication by piecewise continuous matrix functions. The operators of the second type act in the space of real vector functions and, thus, are linear over $\mathbb{R}$. They arise in the direct reduction of elliptic boundary problems using integral representations. A criterion is obtained for these operators to be Fredholm, and a formula for their index is indicated.
Keywords:
singular integral operator, first-order elliptic systems, generalize Cauchy kernels, piecewise smooth contour, index formula.
Citation:
A. P. Soldatov, “Singular integral operators with generalized Cauchy kernel on piecewise smooth contour”, Mathematical notes of NEFU, 28:3 (2021), 70–84
\Bibitem{Sol21}
\by A.~P.~Soldatov
\paper Singular integral operators with generalized Cauchy kernel on piecewise smooth contour
\jour Mathematical notes of NEFU
\yr 2021
\vol 28
\issue 3
\pages 70--84
\mathnet{http://mi.mathnet.ru/svfu326}
\crossref{https://doi.org/10.25587/SVFU.2021.52.22.005}
\elib{https://elibrary.ru/item.asp?id=46670177}
Linking options:
https://www.mathnet.ru/eng/svfu326
https://www.mathnet.ru/eng/svfu/v28/i3/p70
This publication is cited in the following 1 articles:
Nusrat Rajabov, Lutfiya Nusratovna Rajabova, “THREE OVER DETERMINED SYSTEM VOLTERRA TYPE INTEGRAL EQUATION WITH THREE SINGULAR AND SUPER-SINGULAR DOMAINS”, tnusns, 2024:1 (2023)