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This article is cited in 4 scientific papers (total in 4 papers)
Holomorphic extension of functions along finite families of complex straight lines in an $n$-circular domain
A. M. Kytmanova, S. G. Myslivets
a Siberian Federal University, Institute of Mathematics, Krasnoyarsk, Russia
Abstract:
We consider the continuous functions on the boundary of a bounded $n$-circular domain $D$ in $\mathbb C^n$, $n>1$, 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 $D$.
Keywords:
holomorphic extension, $n$-circular domains, Szegö integral representation.
| Funding Agency |
Grant Number |
Russian Foundation for Basic Research  |
14-01-00544 |
| Ministry of Education and Science of the Russian Federation |
14.Y26.31.0006
НШ-9149.2016.1 |
| 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). |
DOI:
https://doi.org/10.17377/smzh.2016.57.406
 Full text:
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English version:
Siberian Mathematical Journal, 2016, 57:4, 618–631
Bibliographic databases:
  
UDC:
517.55
Received: 18.09.2015
Citation:
A. M. Kytmanov, S. G. Myslivets, “Holomorphic extension of functions along finite families of complex straight lines in an $n$-circular domain”, Sibirsk. Mat. Zh., 57:4 (2016), 792–808; Siberian Math. J., 57:4 (2016), 618–631
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/smj2785 http://mi.mathnet.ru/eng/smj/v57/i4/p792
Citing articles on Google Scholar:
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This publication is cited in the following articles:
-
Alexander M. Kytmanov, Simona G. Myslivets, “Multidimensional boundary analog of the Hartogs theorem in circular domains”, Zhurn. SFU. Ser. Matem. i fiz., 11:1 (2018), 79–90
 -
Bayram P. Otemuratov, “On holomorphic continuation of integrable functions along finite families of complex lines in an $n$-circular domain”, Zhurn. SFU. Ser. Matem. i fiz., 11:1 (2018), 91–96
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Simona G. Myslivets, “Functions with the one-dimensional holomorphic extension property”, Zhurn. SFU. Ser. Matem. i fiz., 12:4 (2019), 439–443
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A. M. Kytmanov, S. G. Myslivets, “On functions with one-dimensional holomorphic extension property in circular domains”, Math. Nachr., 292:6 (2019), 1321–1332
 
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