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Holomorphic extension of functions along finite families of complex straight lines in an n-circular domain

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Abstract

We consider the continuous functions on the boundary of a bounded n-circular domain D in ℂn, n > 1, which admit one-dimensional holomorphic extension along a family of complex straight lines passing through finitely many points of D. The question is addressed of the existence of a holomorphic extension of these functions to D.

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Correspondence to A. M. Kytmanov.

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Original Russian Text Copyright © 2016 Kytmanov A.M. and Myslivets S.G.

Krasnoyarsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 4, pp. 792–808, July–August, 2016; DOI: 10.17377/smzh.2016.57.406. Original article submitted September 18, 2015.

The authors were supported by the Russian Foundation for Basic Research (Grant 14–01–00544), the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh–9149.2016.1), and the Government of the Russian Federation for the State Maintenance Program for the Leading Scientific Schools at Siberian Federal University (Grant 14.Y26.31.0006).

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Kytmanov, A.M., Myslivets, S.G. Holomorphic extension of functions along finite families of complex straight lines in an n-circular domain. Sib Math J 57, 618–631 (2016). https://doi.org/10.1134/S0037446616040066

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  • DOI: https://doi.org/10.1134/S0037446616040066

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