Speaker
Description
We consider the problem of continuability into a sectorial domain for multiple
power series in approach when the coeffcients of power series interpolates by values of an entire or a meromorphic functions at the natural numbers.
The growth of the interpolating function describes the sectorial set to which the series sum extends.
We obtain the multivariate version of Le Roy, Lindelof's 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 where the multiple series is analytically extends.
This work was performed at the Saint Petersburg Leonhard Euler International Mathematical Institute
and supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075–15–2022–287).
