Imash kyzy M.
Isometry of the subspaces of solutions of systems of differential equations to the spaces of real functions
Ukr. Mat. Zh. - 2019. - 71, № 8. - pp. 1011-1027
We determine the subspaces of solutions of the systems of Laplace and heat-conduction differential equations isometric to the corresponding spaces of real functions determined on the set of real numbers.
Ukr. Mat. Zh. - 2018. - 70, № 3. - pp. 318-336
We investigate the order of growth of the moduli of arbitrary algebraic polynomials in the weighted Bergman space $A_p(G, h),\; p > 0$, in regions with interior zero angles at finitely many boundary points. We obtain estimations for algebraic polynomials in bounded regions with piecewise smooth boundary.
Ukr. Mat. Zh. - 2018. - 70, № 2. - pp. 151-164
We study the possibility of application of the Faber polynomials in proving some combinatorial identities. It is shown that the coefficients of Faber polynomials of mutually inverse conformal mappings generate a pair of mutually invertible relations. We prove two identities relating the coefficients of Faber polynomials and the coefficients of Laurent expansions of the corresponding conformal mappings. Some examples are presented.