The regular seminar of IMM was held. The head of “Non-harmonic Analysis” department, corr.-member of ANAS, prof. Bilalov gave a talk on “Solvability of the Riemannn problem in weighted Smirnov classes with general weight”.

In the talk, the weighted Smirnov classes with general form weight in bounded and unbounded domains, were obtained. Measurable coefficient homogeneous and inhomogeneous Riemann problems whose argument is piecewise continuous functin were considered in these classes.

In the case of homogenous problem, sufficient conditions on the weight function were found (the weights from Mackenhoupt class satisfy these conditions) and in this case the general solution is structured.

In the case of inhomogeneous problem, the Mackenhoupt conditions was imposed on the weight function, orthogonality conditions for solvability of the inhomogeneous problems in weighted Smirnov classes were found, a formula for the index of the problem was given. Different cases with respect to power form weight functions were considered and specific conditions for degeneration order were found.

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