Riemann Boundary Value Problems with Reflectionon 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.