Geodesic
Continuability of multiple power series into sectorial domain by means of interpolation of coefficients
Ufa mathematical journal, Tome 14 (2022) no. 2, pp. 108-115 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the problem on continuability of a multiple power series centered at the origin of $\mathbb{C}^n$ into a sectorial domain. The condition of the mentioned continuability is given in terms of an entire function interpolating the coefficients of the power series. We estimate the indicator function of the interpolating function with the help of which the sectorial set is determined. More precisely, the growth of the interpolating function on the imaginary subspace describes the sectorial set on which the series sum is continued. In the study we use methods of multivariate complex analysis, in particular, integral representations (Cauchy, Mellin, and Lindelof representations), multidimensional residues and properties of power series.
Keywords: multiple power series, analytic continuation, indicator of entire function, multidimensional residues. 
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A. J. Mkrtchyan. Continuability of multiple power series into sectorial domain by means of interpolation of coefficients. Ufa mathematical journal, Tome 14 (2022) no. 2, pp. 108-115. http://geodesic.mathdoc.fr/item/UFA_2022_14_2_a8/

[1] L. Bieberbach, Analytische Fortsetzung, Springer-Verlag, Berlin, 1955

[2] N.U. Arakelian, “Approximation by entire functions and analytic continuation”, Progress in approximation theory. An international perspective, Proc. International Conference on approximation theory (Tampa, South Florida, USA, 1990), Springer-Verlag, New York, 1992, 295–313

[3] N. Arakelian, W. Luh, J. Muller, Compl. Var. Ellip. Equats., 52:7 (2007), 561–573

[4] G. Pólya., “Untersuchungen über Lücken und Singularitäten von Potenzreihen”, Math. Zeit., 29 (1929), 549–640

[5] A.J. Mkrtchyan, “Continuation of multiple power series in a sectorial domain”, Math. Nach., 292:11 (2019), 2441–2451

[6] Am. Math. Soc., Providence, RI, 1992

[7] V.K. Ivanov., “A characterization of the growth of an entire function of two variables and its application to the summation of double power series”, Matem. Sb., 47(89):1 (1959), 3–16 (in Russian)

[8] Am. Math. Soc., Providence, RI, 1974

[9] Am. Math. Soc., 1992

[10] O. N. Zhdanov, A. K. Tsikh., “Investigation of multiple Mellin-Barnes integrals by means of multidimensional residues”, Siber. Math. J., 39:2 (1998), 281–298