4 papers
Critical cyclicity in Dirichlet-type spaces on the bidisk
Athanasios Beslikas, Pouriya Torkinejad Ziarati
Consider the Dirichlet-type spaces on the bidisc defined by $$\mathcal{D}_β(\mathbb{D}^2)=\Bigg\{f(z_1,z_2)=\sum_{k,l}a_{kl}z_1^kz_2^l\in\mathcal{O}(\mathbb{D}^2): \sum_{k,l\ge 0}|…
Examples of critically cyclic functions in the Dirichlet spaces of the ball
Pouriya Torkinejad Ziarati
In this work, we construct examples of holomorphic functions in $D_2(\B_2)$, the Dirichlet space on $\B_2$, for which there exists an index such that the func…
Cyclicity of Multipliers on the Unit Ball of : A Corona-Based Approach
Pouriya Torkinejad Ziarati
We study the cyclicity of multipliers in Dirichlet-type spaces \( D_α(\mathbb{B}_n) \). Specifically, we show that a multiplier \( f \) analytic on a neighborhood of $\overline{\ma…
Cyclicity in Poletsky-Stessin Weighted Bergman Spaces
Pouriya Torkinejad Ziarati
We study the cyclicity of polynomials in Poletsky-Stessin weighted Bergman spaces on various domains in , including the unit ball, the bidisk, and the complex ellipso…