arXiv subjects

Sibel Sahin

Publications and source records attributed to Sibel Sahin.

11 recordsLinked to original sources

arXiv2025

Approximation numbers of differences of composition operators

In this study we consider the approximation numbers of differences of composition operators acting on the Hardy-Hilbert space H 2 (D). We obtain both upper and lower bounds for these approximation numbers and by applying these general results to composition operators with specific types of symbols, we demonstrate the effect of boundary behaviour over the approximation numbers. Moreover, we use these one-dimensional methods and examples to understand the approximation numbers of differences of composition operators acting on the space H 2 (D 2 ) of the bidisc.

math.FA↗

arXiv2022

Density Property and Composition Operators on $H(b)$ Spaces of Finitely Connected Planar Domains

In this work, the density in $H(b)$ spaces of finitely connected planar domains and the boundedness of composition operators on these function spaces are studied. Density of the algebra $\mathcal{A}(D)$ is considered for both in the cases where the defining function $b$ is an extreme and non-extreme point of the unit ball of $H^\infty(D)$. In the last part boundedness of composition operators on $H(b)$ spaces is considered and as well as a generalization of the unit disk case is given, the boundedness of composition operators with generalized Blaschke symbols over finitely connected domains is characterized.

math.FA↗

arXiv2020

Magnetic Geodesics on the Space of Kähler Potentials

In this work, magnetic geodesics over the space of Kähler potentials are studied through a variational method for a generalized Landau-Hall functional. The magnetic geodesic equation is calculated in this setting and its relation to a perturbed complex Monge-Ampère equation is given. Lastly, the magnetic geodesic equation is considered over the special case of toric Kähler potentials over toric Kähler manifolds.

math.CV↗

arXiv2019

m-Pluripotential Theory on Riemannian Spaces and Tropical Geometry

In this study we extend the concepts of $m$-pluripotential theory to the Riemannian superspace formalism. Since in this setting positive supercurrents and tropical varieties are closely related, we try to understand the relative capacity notion with respect to the intersection of tropical hypersurfaces. Moreover, we generalize the classical quasicontinuity result of Cartan to $m$-subharmonic functions of Riemannian spaces and lastly we introduce the indicators of $m$-subharmonic functions and give a geometric characterization of their Newton numbers.

math.CV↗

arXiv2019

Angular Derivatives and Boundary Values of H(b) Spaces of Unit Ball of $\mathbb{C}^n$

In this work we study deBranges-Rovnyak spaces, $H(b)$, on the unit ball of $\mathbb{C}^n$. We give an integral representation of the functions in $H(b)$ through the Clark measure on $S^n$ associated with $b$. A characterization of admissible boundary limits is given in relation with finite angular derivatives. Lastly, we examine the interplay between Clark measures and angular derivatives showing that Clark measure associated with $b$ has an atom at a boundary point if and only if $b$ has finite angular derivative at the same point.

math.CV↗

arXiv2018

Toric Pluripotential Theory

We study finite energy classes of quasiplurisubharmonic (qpsh) functions in the setting of toric compact K{ä}hler manifolds. We characterize toric qpsh functions and give necessary and sufficient conditions for them to have finite (weighted) energy, both in terms of the associated convex function in R n , and through the integrability properties of its Legendre transform. We characterize Log-Lipschitz convex functions on the Delzant polytope, showing that they correspond to toric qpsh functions which satisfy a certain exponential integrability condition. In the particular case of dimension one, those Log-Lipschitz convex functions of the polytope correspond to H{ö}lder continuous toric quasisubharmonic functions.

math.CV↗

arXiv2016

Beurling-Type Invariant Subspaces of the Poletsky-Stessin Hardy Spaces in the Bidisc

The invariant subspaces of the Hardy space on $H^2(\mathbb{D})$ of the unit disc are very well known however in several variables the structure of the invariant subspaces of the classical Hardy spaces is not yet fully understood. In this study we examine the invariant subspace problem for Poletsky-Stessin Hardy spaces which is a natural generalization of the classical Hardy spaces to hyperconvex domains in $\mathbb{C}^n$. We showed that not all invariant subspaces of $H^{2}_{\tilde{u}}(\mathbb{D}^2)$ are of Beurling-type. To characterize the Beurling-type invariant subspaces of this space we first generalized the Lax-Halmos theorem of vector valued Hardy spaces to the vector valued Poletsky-Stessin Hardy spaces and then we give a necessary and sufficient condition for the invariant subspaces of $H^{2}_{\tilde{u}}(\mathbb{D}^2)$ to be of Beurling-type.

math.CV↗

arXiv2016

Cauchy-Fantappie Type Operators And Duality On Poletsky-Stessin Hardy Spaces of Complex Ellipsoids

In the first part of this study we consider the boundedness and compactness properties of Cauchy-Fantappie type operators on Poletsky-Stessin Hardy spaces $H^{p}_{u}(\mathbb{B}^{\textbf{p}})$ of complex ellipsoids. We show that boundedness and compactness criteria are given by the Carleson conditions. In addition we give a basic compactness property for the subsets of $H^{p}_{u}(\mathbb{B}^{\textbf{p}})$ spaces and the characterization of weakly convergent sequences in $H^{p}_{u}(\mathbb{B}^{\textbf{p}})$. In the second part we will discuss the dual complement of the complex ellipsoid and we will give a duality result for $H^{p}_{u}(\mathbb{B}^{\textbf{p}})$ spaces in the sense of Grothendieck-Köthe-da Silva.

math.CV↗

arXiv2016

Choquet-Monge-Ampere Classes

We introduce and study Choquet-Monge-Ampere classes on compact Kahler manifolds. They consist of quasi-plurisubharmonic functions whose sublevel sets have small enough asymptotic Monge-Ampere capacity. We compare them with finite energy classes, which have recently played an important role in Kahler Geometry.

math.CV↗

arXiv2014

Poletsky-Stessin Hardy Spaces on Complex Ellipsoids in C^n

We study Poletsky-Stessin Hardy spaces on complex ellipsoids in C^n. Different from one variable case, classical Hardy spaces are strictly contained in Poletsky-Stessin Hardy spaces on complex ellipsoids so boundary values are not automatically obtained in this case. We have showed that functions belonging to Poletsky-Stessin Hardy spaces have boundary values and they can be approached through admissible approach regions in the complex ellipsoid case. Moreover, we have obtained that polynomials are dense in these spaces. We also considered the composition operators acting on Poletsky-Stessin Hardy spaces on complex ellipsoids and gave conditions for their boundedness and compactness.

math.CV↗

arXiv2013

Poletsky-Stessin Hardy Spaces on Domains Bounded by An Analytic Jordan Curve in $\mathbb{C}$

We study Poletsky-Stessin Hardy spaces that are generated by continuous, subharmonic exhaustion functions on a domain $Ω\subset\mathbb{C}$, that is bounded by an analytic Jordan curve. Different from Poletsky & Stessin's work these exhaustion functions are not necessarily harmonic outside of a compact set but have finite Monge-Ampére mass. We have showed that functions belonging to Poletsky-Stessin Hardy spaces have a factorization analogous to classical Hardy spaces and the algebra $A(Ω)$ is dense in these spaces as in the classical case ; however, contrary to the classical Hardy spaces, composition operators with analytic symbols on these Poletsky-Stessin Hardy spaces need not always be bounded.

math.CV↗