Related papers: Rational dilation for operators associated with sp…
In this note, we present a characterization of semistable unitary operators on $L^2(\mathbb{R})$, under the assumption that the operator is (i) translation-invariant, (ii) symmetric, and (iii) locally uniformly continuous (LUC) under…
Recent results on the spectral properties of the Hermitian Wilson-Dirac operator are presented.
We find characterization for the distinguished varieties in the symmetrized polydisc $\mathbb G_n \; (n\geq 2)$ and thus generalize the work [\textit{J. Funct. Anal.}, 266 (2014), 5779 -- 5800] on $\mathbb G_2$ by the author and Shalit. We…
In this note, we propose a variational framework in which the minimization of the acceleration on the group of diffeomorphisms endowed with a right-invariant metric is well-posed. It relies on constraining the acceleration to belong to a…
The aim of this paper is to correct a mistake in earlier work on the conformal invariance of Rarita-Schwinger operators and use the method of correction to develop properties of some conformally invariant operators in the Rarita-Schwinger…
Continuity, compactness, the spectrum and ergodic properties of the differentiation operator are investigated, when it acts in the Fr\'echet space of all Dirichlet series that are uniformly convergent in all half-planes $\{s \in \mathbb{C}…
In this article we study different aspects of Hermitian operators applying the concept of positive decompositions. On the one hand, we characterize the positivity of an Hermitian operator by means of a norm condition where the factors of…
We consider a regularization concept for the solution of ill--posed operator equations, where the operator is composed of a continuous and a discontinuous operator. A particular application is level set regularization, where we develop a…
We construct interpolation operators for functions taking values in a symmetric space -- a smooth manifold with an inversion symmetry about every point. Key to our construction is the observation that every symmetric space can be realized…
Researchers have identified complex matrices $A$ such that a bounded linear operator $B$ acting on a Hilbert space will admit a dilation of the form $A \otimes I$ whenever the numerical range inclusion relation $W(B) \subseteq W(A)$ holds.…
We introduce and systematically develop two classes of discrete integrable operators: those with $2\times 2$ matrix kernels and those possessing general differential kernels, thereby generalizing the discrete analogue previously studied. A…
We study approximation properties of general multivariate periodic quasi-interpolation operators, which are generated by distributions/functions $\widetilde{\varphi}_j$ and trigonometric polynomials $\varphi_j$. The class of such operators…
The procedure of evaluating of the spectrum for discrete periodic operators perturbed by operators of smaller dimensions is obtained. This result allows to obtain propagative, guided, localised spectra for different kind of physical…
We consider the problem of interpolating projective varieties through points and linear spaces. We show that del Pezzo surfaces satisfy weak interpolation.
We establish necessary and sufficient conditions for the boundedness and compactness of weighted composition operators acting on weighted Dirichlet spaces and determine the spectrum of a certain class of such operators. Our results extend…
A distinguished variety in the polydisc $\mathbb D^n$ is an affine complex algebraic variety that intersects $\mathbb D^n$ and exits the domain through the $n$-torus $\mathbb T^n$ without intersecting any other part of the topological…
The main purpose of this paper is to study multi-parameter singular integral operators which commute with Zygmund dilations. We introduce a class of singular integral operators associated with Zygmund dilations and show the boundedness for…
The aim of the paper is firstly to study domains of definitions in terms of boundary conditions of minimal and maximal operators, as well as selfadjoint extensions of a minimal operator associated with the fourth-order differential operator…
The worst-case performance of an optimization method on a problem class can be analyzed using a finite description of the problem class, known as interpolation conditions. In this work, we study interpolation conditions for linear operators…
In this paper, we investigate the problem of designing compact support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an infinite nonlinear problem to a finite…