arXiv subjects

Aleksandr Mkrtchyan

Publications and source records attributed to Aleksandr Mkrtchyan.

2 recordsLinked to original sources

arXiv2024

Multivariate analog of the Le Roy-Lindelöf theorem about power series analytic continuation

We consider the problem of continuability into a sectorial domain for multiple power series and prove the multivariate analog of the Le Roy-Lindelöf theorem, i.e. establish a connection between the growth of the holomorphic function interpolating the series coefficients in the imaginary subspace and the sectoral domain where the multiple power series is analytically continued to.

math.CV↗

arXiv2022

Trigonometric Convexity for the Multidimensional Indicator after Ivanov

Multidimensional indicator after Ivanov is a generalization of the notion of indicator, that is well-known for analytic functions in one complex variable, to analytic functions in several complex variables. We prove an analogue of trigonometric convexity for it. Additionally, we show that our estimate is sharp. The proof is based on the multidimensional analogue of the sectorial Fourier inversion formula.

math.CV↗