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Sequences of zeroes of holomorphic functions in weight spaces in the unit disk

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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.

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References

  1. 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).

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  2. 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).

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  3. 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).

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  4. K. Seip, “An Extension of the Blaschke Condition,” J. London Math. Soc. (2) 51(3), 545–558 (1995).

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Correspondence to F. B. Khabibullin.

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Original Russian Text © F.B. Khabibullin, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 3, pp. 102–??.

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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

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  • DOI: https://doi.org/10.3103/S1066369X1003014X

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