Institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan will hold its next weekly seminar on March 06, 2019, 10:00 a.m., which will feature a report by associate professor Migdad Ismailov, senior researcher of the Department of Non-Harmonic Analysis of IMM of the NAS of Azerbaijan, entitled “Some problems of approximation in grand-Lebesgue spaces”.

In the report the subspace G ^p)(-π; π) of the grand-Lebesgue space L^p)(-π; π), p>1. is defined. Density of the set C₀^∞ [-π; π ] of continuous finite  functions on a segment [-π; π ] is established  in space G ^p)(-π; π).The basis properties of trigonometric systems and exponential systems in space G ^p)(-π; π), p>1 are studied. H_p)^± grand-Hardy classes of analytic functions in the unit circle are defined. The necessary and sufficient conditions are found for the validity of the analogs of the classical Riesz, Smirnov theorems and the Cauchy formula in these classes.

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