Athanasios Beslikas

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20242026

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math.CV2026

Composition operators and Rational Inner Functions on the bidisc: A geometric approach

Athanasios Beslikas

We study composition operators acting on the weighted Bergman spaces on the bidisc, i.e. $C_{Φ} : A_{β}^{2} (D^{2}) \to A_{β}^{2} (D^{2})$ where $Φ$ is induced by rational inner fun…

math.CV2025

On the membership of two-variable Rational Inner Functions in spaces of Dirichlet-type

Athanasios Beslikas, Alan Sola

We study membership of rational inner functions on the bidisk $D^{2}$ in a scale of Dirichlet spaces considered by Bera, Chavan, and Ghara, and in higher-order variants of t…

math.CV2025

Composition Operators and Rational Inner Functions II: Boundedness between two different Bergman Spaces

Athanasios Beslikas

In this note we provide a sufficient condition on when the composition operator $C_{Φ} : A_{a}^{2} (D^{2}) \to A_{β}^{2} (D^{2})$ is bounded, whenever $a \geq - 1$ and $β$ is positive…

math.CV2024

Composition operators and Rational Inner Functions on the bidisc

Athanasios Beslikas

In the present article, composition operators induced by Rational Inner Functions on the bidisc $D^{2}$ are studied, acting on the weighted Bergman space $A^2_β(\mathbb{D}^2…