Veselovska H. Pade type approximations of special functions of several variables

The thesis is devoted to investigations of problems of existence of multidimensional generalized moment representations and problems of construction of Pade type approximants of functions of several variables by the method of multidimensional generalized moment representations. In our research, the method of multidimensional generalized moment representations is extended to new broad classes of functions of two variables for which coefficients of power expansion have two-dimensional generalized moment representations in operator form providing some special choice of linear bounded operators. For each of the classes considered, their representations are constructed through the resolvent functions of the chosen linear bounded operators. In particular, one of those functions that belong to the considered classes are certain two-variable hypergeometric functions of the second, third, and fourth order. The efficiency of the constructed approximation is illustrated by examples using graphs and tables. For one of the classes of functions of two variables, the uniform convergence of constructed Pade type approximants is proved as well as the asymptotic behavior of the numerators and the denominators is examined.