The Riemann–Hilbert Boundary Value Problem with a Countable Set of Coefficient Discontinuities and Two-side Curling at Infinity of the Order Less Than 1/2
The Riemann–Hilbert boundary value problem is one of the oldest boundary value problems of theory of analytic functions.Its complete solution (for the case of a finite index and continuous coefficients) was given by Hilbert in 1905.I n the present paper we study the inhomogeneous Riemann–Hilbert boundary value problem in the upper half of complex plane with strong singularities of boundary data.W e obtain general solution for the case where coefficients of the problem have a countable set of finite discontinuity points and two-side curling of order less than 1/2 at the infinity point.W e investigate also the solvability conditions.
KeywordsRiemann–Hilbert boundary value problem infinite index curlings entire functions
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