Multivariate Analog of the Le Roy–Lindelöf Theorem about Power Series Analytic Continuation

The problem of continuation of multiple power series into a sectorial domain is considered and a multivariate analogue of the Le Roy–Lindelöf theorem is proved, i.e., a connection is established between the growth of a holomorphic function interpolating the coefficients of the series in an imaginary subspace and the sectoral domain, where the multiple power series is analytically continued.