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Theorem concerning analytic continuation
Authors:A. M. Lukatskii
Affiliation:(1) M. V. Lomonosov Moscow State University, USSR
Abstract:A. I. Markushevich obtained the following representation of a function in its holomorphicity star with a sequence {mv}, for which mv+1/mvrarrinfin: Here it is proved that this condition is necessary; more precisely,
$$overline {mathop {lim }limits_{v to infty } } frac{{m_{v + 1} }}{{m_v }} = infty $$
. This result is derived from certain properties of over-convergent power series.Translated from Matematicheskie Zametki, Vol. 10, No. 1, pp. 57–62, July, 1971.The author wishes to thank his scientific director A. I. Markushevich for his advice concerning this work.
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