About restory of analytic functions in the Mittag-Leffler’s spiral star by the values on a set of uniqueness

In the case of one complex variable, many traditional set of uniqueness in the class of analytic functions is the set containing the limit point. The most famous variety of uniqueness in the multivariate case is a “real” neighborhood of a point. For a certain class of many domains of uniqueness in the multidimensional case can be reduced. For example, in the works of S. V. Znamenskii a countable subset on the skeleton of polydisc, the value of a holomorphic function is restored throughout polydisc are specified. Perhaps the function can be continued in a larger area. In the works of J. Hadamard, G. Mittag-Lefler, Le Roy, Lindelof the so-called summation methods that give good results for analytic continuation of a power series in the case of star fields of the complex plane have been proposed. Further, for the one-dimensional case, in the works of N. At. Arakelyan the restoration of the analytical element using the universal matrix methods of summation in class helical regions was obtained. The present work is devoted to the restoration of analytic functions defined on a countable set of uniqueness skeleton of polydisc, in the helical region, called (m,α) is the star of the Mittag-Lefler of this function. Recovery is carried out using multidimensional matrix methods of summation of multiple power series, which are constructed using one-dimensional matrix methods of summation of power series. While testing a multivariate matrix methods of summation of multiple power series are performed using a one-dimensional exponentially.