Geodesic
Holomorphic continuation of functions along finite families of complex lines in the ball
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 4, pp. 547-557

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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 study the problem of existence of holomorphic continuation of such functions in a ball $B$.
Keywords: holomorphic continuation
Mots-clés : Poisson integral. 
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     author = {Alexander M. Kytmanov and Simona G. Myslivets},
     title = {Holomorphic continuation of functions along finite families of complex lines in the ball},
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Alexander M. Kytmanov; Simona G. Myslivets. Holomorphic continuation of functions along finite families of complex lines in the ball. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 5 (2012) no. 4, pp. 547-557. http://geodesic.mathdoc.fr/item/JSFU_2012_5_4_a10/