Displaying similar documents to “Composition operators on the Dirichlet space and related problems.”

Composition operators in the Dirichlet series setting

Hervé Queffélec (2007)

Banach Center Publications

Similarity:

In this work, we begin with a survey of composition operators on the Hardy space H² and on the Wiener algebra A⁺ of absolutely convergent Taylor series, with special emphasis on their compactness, or invertibility, or isometric character. The main results are due respectively to J. Shapiro and D.~Newman. In a second part, we present more recent results, due to Gordon and Hedenmalm on the one hand, and to Bayart, the author et al. on the other hand, concerning the analogues of H² and...

Compact differences of composition operators on weighted Dirichlet spaces

Robert Allen, Katherine Heller, Matthew Pons (2014)

Open Mathematics

Similarity:

Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces . Specifically we study differences of composition operators on the Dirichlet space and S 2, the space of analytic functions whose first derivative is in H 2, and then use Calderón’s complex interpolation to extend the results to the general weighted Dirichlet spaces. As a corollary we consider composition operators induced by linear fractional self-maps of the disk. ...

An extension of the univalence criterion for a family of integral operators

Erhan Deniz, Halit Orhan (2010)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

Similarity:

The main object of the present paper is to extend the univalence condition for a family of integral operators. Relevant connections of some of the results obtained in this paper with those in earlier works are also provided.

Reducibility and unitary equivalence for a class of multiplication operators on the Dirichlet space

Yong Chen, Young Joo Lee, Tao Yu (2014)

Studia Mathematica

Similarity:

We consider the reducibility and unitary equivalence of multiplication operators on the Dirichlet space. We first characterize reducibility of a multiplication operator induced by a finite Blaschke product and, as an application, we show that a multiplication operator induced by a Blaschke product with two zeros is reducible only in an obvious case. Also, we prove that a multiplication operator induced by a multiplier ϕ is unitarily equivalent to a weighted shift of multiplicity 2 if...

On Dirichlet type spaces on the unit ball of C n

Małgorzata Michalska (2011)

Annales UMCS, Mathematica

Similarity:

In this paper we discuss characterizations of Dirichlet type spaces on the unit ball of Cn obtained by P. Hu and W. Zhang [2], and S. Li [4].

Some Hilbert spaces related with the Dirichlet space

Nicola Arcozzi, Pavel Mozolyako, Karl-Mikael Perfekt, Stefan Richter, Giulia Sarfatti (2016)

Concrete Operators

Similarity:

We study the reproducing kernel Hilbert space with kernel kd , where d is a positive integer and k is the reproducing kernel of the analytic Dirichlet space.