The main goal of this paper is to prove the following statement. Let f = ∑n∈E anz be a function holomorphic and of bounded characteristic in the unit disk D, where E is a ∧(1)-subset of ℤ+. Assume that f has a pseudocontinuation of bounded characteristic to the annulus {z ∈ ℂ : 1 < |z| < R}. Then f admits analytic continuation to the disk RD. In particular, f is a polynomial if R = +∞. Bibliography: 16 titles.
Original language | English |
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Pages (from-to) | 3550-3559 |
Number of pages | 10 |
Journal | Journal of Mathematical Sciences |
Volume | 92 |
Issue number | 1 |
DOIs | |
State | Published - 1998 |
Externally published | Yes |
ID: 87312466