Geodesic
Lacunary series and pseudocontinuations
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 24, Tome 232 (1996), pp. 16-32

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The main aim of this paper is to prove the following assertion. Let $f=\sum_{n\in E}a_nz^n$ be a function holomorphic and of bounded characteristic in the unit disk $\mathbb D$ where $E$ is a $\Lambda(1)$-subset of $\mathbb Z_+$. Suppose $f$ has a pseudocontinuation of bounded characteristic in an annulus $\{z\in\mathbb C\colon1|z|$. Then $f$ admits analytic continuation to the disk $R\mathbb D$. In particular, $f$ is a polynomial if $R=+\infty$. Bibl. 16 titles. 
@article{ZNSL_1996_232_a1,
     author = {A. B. Aleksandrov},
     title = {Lacunary series and pseudocontinuations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {16--32},
     publisher = {mathdoc},
     volume = {232},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1996_232_a1/}
}
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A. B. Aleksandrov. Lacunary series and pseudocontinuations. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 24, Tome 232 (1996), pp. 16-32. http://geodesic.mathdoc.fr/item/ZNSL_1996_232_a1/