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arXiv · 2405.03020

Non-cyclicity and polynomials in Dirichlet-type spaces of the unit ball

Dimitrios Vavitsas·Konstantinos Zarvalis
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Abstract

We give a description of the intersection of the zero set with the unit sphere of a zero-free polynomial in the unit ball of $\mathbb{C}^n$. This description leads to the formulation of a conjecture regarding the characterization of polynomials that are cyclic in Dirichlet-type spaces in the unit ball of $\mathbb{C}^n$. Furthermore, we answer partially ascertaining whether an arbitrary polynomial is not cyclic.

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Dimitrios Vavitsas, Konstantinos Zarvalis. 2024-05-05. Non-cyclicity and polynomials in Dirichlet-type spaces of the unit ball. https://arxiv.org/abs/2405.03020

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