Geodesic
Holomorphic extension of continuous functions along finite families of~complex lines in a ball
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 8 (2015) no. 3, pp. 291-302

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In this paper we consider continuous functions given on the boundary of a ball $B$ of $\mathbb C^n$, $n>1$, and having one-dimensional property of holomorphic extension along the families of complex lines, passing through finite number of points of $B$. We prove the existence of holomorphic extension of such functions in the ball $B$.
Keywords: holomorphic extension, complex lines.
Mots-clés : Poisson kernel 
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Alexander M. Kytmanov; Simona G. Myslivets. Holomorphic extension of continuous functions along finite families of~complex lines in a ball. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 8 (2015) no. 3, pp. 291-302. http://geodesic.mathdoc.fr/item/JSFU_2015_8_3_a4/