Discussions on the solvability of the Riemann problem in the Smirnov classes held

25.04.2018 08:25

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Discussions on the solvability of the Riemann problem in the Smirnov classes held

The Institute of Mathematics and Mechanics of ANAS held next seminar on April 25, 2018,

At the seminar, head of the Department of Non-Harmonic Analysis of ANAS, corresponding member of ANAS, Professor Bilal Bilalov delivered paper “On solvability of Riemann problem in weighted Smirnov classes with general weight”.

Weighted Smirnov classes with general weight for bounded and unbounded domains are defined in the report. Homogeneous and non-homogeneous Riemann problems with a measurable coefficient whose argument is a piecewise-continuous function are considered in these classes.

In case of homogeneous problem, sufficient conditions for the weight function are found (Muckenhoupt weights satisfy these conditions) and a general solution of this problem is constructed. In case of non-homogeneous problem, Muckenhoupt-type condition is imposed on the weight function, the orthogonality condition for the solvability of non-homogeneous problem in weighted Smirnov classes is found, and a formula for the index of the problem is derived. Special cases of power weight functions are considered and conditions for degeneracy order are found.

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