Institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan will hold its next weekly seminar on April 25, 2018, 10:00 a.m., which will feature a report by professor Bilal Bilalov, corresponding member of the NAS of Azerbaijan and the head of the Department of Non-Harmonic Analysis of IMM of the NAS of Azerbaijan, entitled “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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