On multidimensional Jackson's theorem

We have found the best linear polynomial methods of approximation of continuous periodic functions of multiple variables in uniform metric with concave modulus of continuity.

The best polynomial approximations of some classes of analytic functions in the Hardy spaces

Problems of the best polynomial approximation of classes of analytic functions $$$H^m_{p,R}$$$, $$$m\in \mathbb{Z}_+$$$, $$$R \geqslant 1$$$, $$$1 \leqslant p \leqslant \infty$$$, have been investigated in the Hardy spaces $$$H_p$$$. The best linear methods of approximation were constructed on the indicated classes.

Multivalued monotone stochastic differential equations with jumps

We study multivalued stochastic differential equations (MSDEs) with maximal monotone operators driven by semimartingales with jumps. We discuss in detail some methods of approximation of solutions of MSDEs based on discretization of processes and Yosida approximation of the monotone operator. We also study the general problem of stability of solutions of MSDEs with respect to the convergence of driving semimartingales.