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Abstract: In this paper we consider the spectral problem for the CauchyRiemann operator with Bicadze Samarskii type boundary value conditions, reduced to a singular integral equation with continuous kernel. Moreover, we characterize those spectral parameters at which the inhomogeneous boundary value problem with shift into the region for Cauchy-Riemann equations is everywhere solvable in the class of continuous functions on the unit circle.

ON AN INHOMOGENEOUS BOUNDARY VALUE PROBLEM WITH SHIFT INTO THE REGION FOR THE CAUCHY-RIEMANN EQUATIONS WITH SPECTRAL PARAMETER