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JOURNALS // Journal of Siberian Federal University. Mathematics & Physics // Archive

J. Sib. Fed. Univ. Math. Phys., 2013 Volume 6, Issue 3, Pages 329–335 (Mi jsfu318)

Power Series Nonextendable Across the Boundary of their Convergence Domain

Aleksandr D. Mkrtchyanab

a Faculty of Mathematics and Mechanics, Yerevan State University, Yerevan, Armenia
b Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk, Russia

Abstract: In the article we construct a new power series in a single variable nonextendable through the boundary circle of the convergence disk. This series refines the known Fredholm`s example.
Using this series we construct a double power series that does not admit an analytic continuation across the boundary of its convergence domain.

Keywords: power series, analitic continuation, infinitely differentiate, Dirichlet series.

UDC: 517.55

Received: 10.03.2013
Received in revised form: 14.04.2013
Accepted: 20.05.2013

Language: English



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