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Lacunary series and pseudocontinuations

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Abstract

The main goal of this paper is to prove the following statement. Let\(f = \sum\limits_{n \in E} {a_n z^n } \) be a function holomorphic and of bounded characteristic in the unit disk\(\mathbb{D}\), where E is a Λ(1)-subset of ℤ+. Assume that f has a pseudocontinuation of bounded characteristic to the annulus {zɛℂ:1<|z|<R}. Then f admits analytic continuation to the disk R\(\mathbb{D}\). In particular, f is a polynomial if R=+∞. Bibliography: 16 titles.

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Authors
  1. A. B. Aleksandrov
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Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 232, 1996, pp. 16–32.

Translated by A. B. Aleksandrov.

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Aleksandrov, A.B. Lacunary series and pseudocontinuations. J Math Sci 92, 3550–3559 (1998). https://doi.org/10.1007/BF02440139

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