Related papers: Inner functions and operator theory
A regular generalized sampling theory in some structured T-invariant subspaces of a Hilbert space H, where T denotes a bounded invertible operator in H, is established in this paper. This is done by walking through the most important cases…
This is a review paper based on the series of our papers devoted to a structure of true-poly-analytic Bergman function spaces over the upper half-plane in the complex plane and to a detailed study of properties of Toeplitz operators with…
We introduce a generalized Crofoot transform between the model spaces corresponding to matrix-valued inner functions. As an application, we obtain results about matrix-valued truncated Toeplitz operators.
We discuss some basic problems and conjectures in a program to construct general orbifold conformal field theories using the representation theory of vertex operator algebras. We first review a program to construct conformal field theories.…
The behavior of certain weighted Hardy-type operators on rearrangement-invariant function spaces is thoroughly studied with emphasis being put on the optimality of the obtained results. First, the optimal rearrangement-invariant function…
Functional analysis, especially the theory of Hilbert spaces and of operators on these, form an important area in mathematics. We formalized the Isabelle/HOL library Complex_Bounded_Operators containing a large amount of theorems about…
The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the…
This article aims to explore the most recent developments in the study of the Hilbert matrix, acting as an operator on spaces of analytic functions and sequence spaces. We present the latest advances in this area, aiming to provide a…
The use of a tensor product perspective has enriched functional analysis and other important areas of mathematics and physics. The context of operator spaces is clearly no exception. The aim of this manuscript is to kick off the development…
Linear spaces with an Euclidean metric are ubiquitous in mathematics, arising both from quadratic forms and inner products. Operators on such spaces also occur naturally. In recent years, the study of multivariate operator theory has made…
A characterisation is given of bounded embeddings from weighted $L^2$ spaces on bounded intervals into $L^2$ spaces on the half-plane, induced by isomorphisms given by the Laplace transform onto weighted Hardy and Bergman spaces (Zen…
We identify subsets of the joint numerical range of an operator tuple in terms of its joint spectrum. This result helps us to transfer weak convergence of operator orbits into certain approximation and interpolation properties for powers in…
We discuss the range spaces of Toeplitz operators with co-analytic symbols where we focus on the boundary behavior of the functions in these spaces as well as a natural orthogonal decomposition of this range.
This survey aims to give a brief introduction to operator theory in the Hardy space over the bidisc $H^2(\mathbb D^2)$. As an important component of multivariable operator theory, the theory in $H^2(\mathbb D^2)$ focuses primarily on two…
We study the notion of recurrence and some of its variations for linear operators acting on Banach spaces. We characterize recurrence for several classes of linear operators such as weighted shifts, composition operators and multiplication…
We investigate some types of composition operators, linear and not, and conditions for some spaces to be mapped into themselves and for the operators to satisfy some good properties.
In this paper we introduce the systematic study of invariant functions and equivariant mappings defined on Minkowski space under the action of the Lorentz group. We adapt some known results from the orthogonal group acting on the Euclidean…
We study algebraic properties of Toeplitz operators on Bergman spaces of polyanalytic functions on the unit disk. We obtain results on finite-rank commutators and semi-commutators of Toeplitz operators with harmonic symbols. We also raise…
We consider three problems connected with coinvariant subspaces of the backward shift operator in Hardy spaces $H^p$: 1) properties of truncated Toeplitz operators; 2) Carleson-type embedding theorems for the coinvariant subspaces; 3)…
In this paper we introduce the class of matrix valued asymmetric truncated Hankel operators. By using characterizations of matrix valued asymmetric truncated Toeplitz operators, we characterize matrix valued asymmetric truncated Hankel…