Continuation of multiple power series in a sectorial domain

Abstract

For multiple power series centered at the origin we consider the problem of its analytic continuability into a sectorial domain. The condition for continuability is formulated in terms of a holomorphic function that interpolates the series coefficients. For series in one variable this problem has been studied in the works of E. Lindelöf, N. Arakelian, and others.

Continuability of multiple power series into sectorial domain by means of interpolation of coefficients

“…In the multivariable case, for some classes of power series, in [5] a condition for continuability into a sectorial domain was given in terms of a holomorphic function that interpolated the series coefficients.…”