Geodesic
On holomorphic continuation of functions defined on a~pencil of~boundary complex lines
Izvestiya. Mathematics , Tome 69 (2005) no. 2, pp. 345-363

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We study domains of holomorphy of functions having thin singularities along a fixed direction. We prove a boundary analogue of Hartogs' theorem on the holomorphic continuation of functions of several variables that admit holomorphic continuation in one variable. 
@article{IM2_2005_69_2_a3,
     author = {S. A. Imomkulov},
     title = {On holomorphic continuation of functions defined on a~pencil of~boundary complex lines},
     journal = {Izvestiya. Mathematics },
     pages = {345--363},
     publisher = {mathdoc},
     volume = {69},
     number = {2},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2005_69_2_a3/}
}
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S. A. Imomkulov. On holomorphic continuation of functions defined on a~pencil of~boundary complex lines. Izvestiya. Mathematics , Tome 69 (2005) no. 2, pp. 345-363. http://geodesic.mathdoc.fr/item/IM2_2005_69_2_a3/