On analytic continuation of multiple power series beyond the domain of convergence

摘要

In this paper we study the sets of regularity on the boundary of the domain of convergence for a given multiple power series. As such sets we consider collections of polyarcs on the frames of polydisk of convergence of the series. In terms of an entire function, interpolating the coefficients of series, we find the sizes of polyarcs, constituting the regular set. To compute the sizes of polyarcs we essentially use the set of linear majorants for the logarithm of the module of interpolating entire function.