Speaker
Description
We consider the problem of analytic continuation of power series in the sectoral domain by means of interpolation of coefficients by holomorphic functions. We explore the relationship between the growth (indicator) of the interpolating function and the set, to which the series can be extended.
To estimate the growth of a holomorphic function of several complex variables, we use a multidimensional indicator
after Ivanov, which is one of generalizations of the indicator introduced by Phragmén and Lindelöf for analytic
functions of one complex variable. Also, a piecewise affine majorant for some subclass of functions will be used.
We obtain a multivariate version of the Le Roy and Lindelöf theorem, i.e., establish a connection between the growth of the interpolating function of the coefficients on the imaginary subspace and the multivariate sectoral domain to which the multiple series extends analytically.
