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Nonuniqueness Sequences for Weighted Algebras of Holomorphic Functions in the Unit Circle

Authors:	L Yu Cherednikova

Institution:	(1) Bashkir State Agrarian University, Bashkir, Russia

Abstract:	Suppose that $\mathcal{P}$ is a system of continuous subharmonic functions in the unit disk $\mathbb{D}$ and $\mathbb{A}_\mathcal{P}$ is the class of holomorphic functions f in $\mathbb{D}$ such that log\|f(z)\| ≤ B _f p _f(z) + C _f, z ∈ $\mathbb{D}$ , where B _f and C _f are constants and p _f ∈ $\mathcal{P}$ . We obtain sufficient conditions for a given number sequence Λ = { λ_n} ⊂ $\mathbb{D}$ to be a subsequence of zeros of some nonzero holomorphic function from $\mathbb{A}_\mathcal{P}$ , i.e., Λ is a nonuniqueness sequence for $\mathbb{A}_\mathcal{P}$ .__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 775–787.Original Russian Text Copyright ©2005 by L. Yu. Cherednikova.

Keywords:	weighted algebra of holomorphic functions continuous subharmonic function nonuniqueness sequence Riesz mass distribution Jensen measure Poisson-Jensen formula
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