Application of geometrical methods in control theory, Mathematical applications in biosciences, economic and etc.

My mathematical work is primary connected with the approximation theory. Other areas of interest are varying fields of analysis, analytic number theory, numerical methods and mathematical modeling. I am also interested in the theory and application of the electoral systems, election conduct and observation.

I carry out research mostly in the field of approximation theory. In the recent years I have been particularly interested in establishing a precise and useful characterization of the rate of convergence of various approximation processes generated either by linear operators or by non-linear as best (weighted) approximation by algebraic or trigonometric polynomials. My research also includes interpolation, (generalized) Fourier expansions, orthogonal polynomials, quadrature formulae, multipliers, application of Fourier analysis in approximation theory, and functional analysis.

Numerical methods for nonlinear partial differential equations – finite element and finite difference methods; algorithms and scientific software; Numerical analysis of nonlinear and spectral problems in hydrodynamics, quantum mechanics, nonlinear heat - conducting medium; Numerical investigation of solutions to generalized Boussinesq’s type equations; Global solvability or finite time blow up of Cauchy problem for generalized Boussinesq’s type equations.

Numerical methods; Approximation theory; Spline-functions; Interpolation and approximation by radon projection data; Aproximating harmonic functions through Radon projections; Low rank approximations.