Geodesic
On Meromorphic Continuation in a Fixed Direction
Matematičeskie zametki, Tome 86 (2009) no. 3, pp. 323-327

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In the present paper, we prove a local boundary version of the well-known Rothstein lemma about the meromorphic continuation with respect to one of the complex variables. The statement is simple, and the proof is based on the well-known Hadamard formulas for the radii of meromorphy, on recent results of Imomkulov about the boundary properties of sequences of plurisubharmonic functions, and on the Rothstein lemma.
Keywords: meromorphic function, meromorphic continuation, analytic function, subharmonic function, plurisubharmonic function, radius of meromorphy
Mots-clés : Hadamard determinant. 
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     author = {A. A. Atamuratov},
     title = {On {Meromorphic} {Continuation} in a {Fixed} {Direction}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {323--327},
     publisher = {mathdoc},
     volume = {86},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_3_a0/}
}
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A. A. Atamuratov. On Meromorphic Continuation in a Fixed Direction. Matematičeskie zametki, Tome 86 (2009) no. 3, pp. 323-327. http://geodesic.mathdoc.fr/item/MZM_2009_86_3_a0/