Related papers: Some notes about distribution frame multipliers
We introduce Riesz potentials for non-Lebesgue measurable functions by taking the integrals in the sense of Choquet with respect to Hausdorff content and prove boundedness results for these operators. Some earlier results are recovered or…
We study the range of time-frequency localization operators acting on modulation spaces and prove a lifting theorem. As an application we also characterize the range of Gabor multipliers, and, in the realm of complex analysis, we…
The description of all correct restrictions of the maximal operator are considered in a Hilbert space. A class of correct restrictions are obtained for which a similar transformation has the domain of the fixed correct restriction. The…
Modeling has become a widespread, useful tool in mathematics applied to diverse fields, from physics to economics to biomedicine. Practitioners of modeling may use algebraic or differential equations, to the elements of which they attribute…
Some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given.
The operator-valued multiplier theorems in weighted abstract Besov spaces are studied. These results permit us to show embedding theorems in weighted Besov-Lions type spaces. The most regular class of interpolation space is found such that…
We characterize bounded multiplication operators in weighted Dirichlet spaces that are power bounded, Ces\`{a}ro bounded and uniformly Kreiss. Moreover, we show the equivalence in such spaces between mean ergodicity and Ces\`{a}ro…
The main purpose of this paper is to investigate the behaviour of fractional integral operators associated to a measure on a metric space satisfying just a mild growth condition, namely that the measure of each ball is controlled by a fixed…
A subset $M$ of a separable Hilbert space $H$ is $\ell^1$-bounded if there exists a Riesz basis $\mathcal{F} = \{e_n\}_{n \in \mathbb{N}}$ for $H$ such that $\sup_{x \in M} \sum_{n \in \mathbb{N}} |\langle x, e_n\rangle| < \infty.$ A…
For applications like the numerical solution of physical equations a discretization scheme for operators is necessary. Recently frames have been used for such an operator representation. In this paper, we apply fusion frames for this task.…
We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…
The problem of distributed matrix multiplication with straggler tolerance over finite fields is considered, focusing on field sizes for which previous solutions were not applicable (for instance, the field of two elements). We employ…
Measures with values in the set of sesquilinear forms on a subspace of a Hilbert space are of interest in quantum mechanics, since they can be interpreted as observables with only a restricted set of possible measurement preparations. In…
In this paper, the main aim is to consider the mapping properties of the maximal or nonlinear commutator for the fractional maximal operator with the symbols belong to the Lipschitz spaces on variable Lebesgue spaces in the context of…
Operator matrices have played a significant role in studying Hilbert space operators. In this paper, we discuss further properties of operator matrices and present new estimates for the operator norms and numerical radii of such operators.…
In the context of variable exponent Lebesgue spaces equipped with a lower Ahlfors measure we obtain weighted norm inequalities over bounded domains for the centered fractional maximal function and the fractional integral operator.
Continuous frames and tensor products are important topics in theoretical physics. This paper combines those concepts. We derive fundamental properties of continuous frames for tensor product of Hilbert spaces. This includes, for example,…
Recent work in Dynamical Sampling has been centered on characterizing frames obtained by the orbit of a vector under a bounded operator. We prove a necessary and sufficient condition for a pair of bounded commuting operators on a separable…
We consider bounded linear operators acting on the $\ell_2$ space indexed by the nodes of a homogeneous tree. Using the Cuntz relations between the primitive shifts on the tree, we generalize the notion of the single-scale time-varying…
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…