Riemann Boundary Value Problems with Reflection on the Real Axis and Related Singular Integral Equations


We prove a theorem on the equivalence of a scalar Riemann boundary value problem with a shift-reflection on the real axis and a matrix Riemann boundary value problem without the shift. A relationship between the boundary value problem in question and a boundary value problem with orientation-preserving shift-rotation on the unit circle is established. The operator identities constructed by the present authors in their preceding papers and permitting one to eliminate the shift-reflection from the integral equation corresponding to the boundary value problem are the main research tool.

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Correspondence to A. A. Karelin or A. A. Tarasenko.

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Translated by V. Potapchouck

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Karelin, A.A., Tarasenko, A.A. Riemann Boundary Value Problems with Reflection on the Real Axis and Related Singular Integral Equations. Diff Equat 57, 100–110 (2021). https://doi.org/10.1134/S0012266121010080

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