Dekanov S. Tauberian and Mercerian theorems for some methods of summation of functions of several variables

The thesis is dedicated, on the one hand, to elucidation of necessary and sufficient conditions in some Mercerian theorems, to generalization of this theorems on Banakh sequences and functions and to generalization of one theorem of Rogosinski'es by means of changing of the constant coefficients in a series by functions. On the other hand, the concept of statistical convergence of the numerical sequence was generalized on simple and double sequences from the real Hausdorff locally convex linear topological space L. After that the statistical (in which statistical convergence of the means instead of plain convergence is taken) D-properties (so to say, the sources of Tauberian theorems) were found and the statistically forced Tauberian theorems with a remainder for simple summation methods of type of Holder and Cesaro methods, of Voronoї of the class WQ and for the double summation methods of Riesz and Voronoї of the class WQ2, defined over the space L, were proved.