Abstract
Let \( \mathbb{D} \) be the unit disk in the complex plane ℂ and let H be a certain weight class of functions holomorphic in \( \mathbb{D} \). We establish conditions under which a given sequence of points A = »k ⊂ \( \mathbb{D} \) is the sequence of zeroes of a holomorphic function from H.
Similar content being viewed by others
References
F. A. Shamoyan, “A Factorization Theorem of M. M. Dzhrbashyan and a Characteristic of the Zeros of Analytic Functions in the Disk with a Majorant of Finite Growth,” Izv. AN Arm. SSR, Mat. 13(5-6), 405–422 (1978).
B. N. Khabibullin, F B. Khabibullin, and L. Yu. Cherednikova, “Zero Subsequences for Classes of Holomorphic Functions: Stability and the Entropy of Arcwise Connectedness,” Algebra i Analiz 20(1), 190–236 (2008).
E. G. Kudasheva and B. N. Khabibullin, “The Distribution of the Zeros of Holomorphic Functions of Moderate Growth in the Unit Disc and the Representation of Meromorphic Functions There,” Matem. Sborn. 200(9), 95–126(2009).
K. Seip, “An Extension of the Blaschke Condition,” J. London Math. Soc. (2) 51(3), 545–558 (1995).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © F.B. Khabibullin, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 3, pp. 102–??.
About this article
Cite this article
Khabibullin, F.B. Sequences of zeroes of holomorphic functions in weight spaces in the unit disk. Russ Math. 54, 88–90 (2010). https://doi.org/10.3103/S1066369X1003014X
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S1066369X1003014X