Dimitrios Vavitsas

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math.CV2026

An overview of cyclicity in Dirichlet-type spaces in the unit ball

Dimitrios Vavitsas

We shall discuss the characterization of cyclicity of polynomials in Dirichlet-type spaces in the Euclidean unit ball of $C^{n}$ which remains an open problem.

math.CV2026

Boundary zeros of stable polynomials in the unit ball

Dimitrios Vavitsas, Jujie Wu, Konstantinos Zarvalis

Interpolation theory in the unit ball and semi-algebraic geometry yield explicit descriptions of the boundary zeros of stable polynomials. Given a polynomial $p\in \mathbb{C}[z_1,…

math.CV2026

Riesz $I^\pm$ -capacity of Cantor sets and cyclicity in Dirichlet-type spaces

Dimitrios Vavitsas, Jujie Wu, Konstantinos Zarvalis

We examine the threshold of the cyclicity for functions in Dirichlet-type spaces $D_{I^} \pm$ , $I^\pm \in (0, 1]$ . Given a fixed $I^\pm^{*} \in (0, 1]$ , we construct a holomorphic function…

math.CV2024

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

Dimitrios Vavitsas, Konstantinos Zarvalis

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 $C^{n}$ . This description leads to the formulati…

An overview of cyclicity in Dirichlet-type spaces in the unit ball

Boundary zeros of stable polynomials in the unit ball

Riesz I^±-capacity of Cantor sets and cyclicity in Dirichlet-type spaces

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

Riesz $I^\pm$ -capacity of Cantor sets and cyclicity in Dirichlet-type spaces