11-16 December 2023
St. Petersburg University, MCS faculty
Europe/Moscow timezone

Analytic continuation of power series by means of coefficients interpolation

13 Dec 2023, 10:00
35m
MCS 201 (SPBU MCS)

MCS 201

SPBU MCS

Russia, 199178, St. Petersburg, 14 line V.O., 29B, https://math-cs.spbu.ru/en/ Room 201 ZOOM streaming at: https://us02web.zoom.us/j/675315555?pwd=aEVYbHZWL2F0aE9PUXVYUjB4a21ydz09

Speaker

Alex Mkrtchyan (Siberian Federal university and Institute of Mathematics NAS RA)

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.

Primary author

Alex Mkrtchyan (Siberian Federal university and Institute of Mathematics NAS RA)

Presentation Materials

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