Related papers: Matrix representations of multidimensional integra…

We define a C*-hull for a *-algebra, given a notion of integrability for its representations on Hilbert modules. We establish a local-global principle which, in many cases, characterises integrable representations on Hilbert modules through…

We compute the spectrum of the operator of multiplication by the complex coordinate in a Hilbert space of holomorphic functions on a disk with two circular holes. Additionally we determine the structure of the $C^*$-algebra generated by…

A C*algebra A generated by a class of zero-order classical pseudodifferential operator on a cylinder RxB, where B is a compact riemannian manifold, containing operators with periodic symbols, is considered. A description of the K-theory…

We establish a Fredholm criterion for an arbitrary operator in the Banach algebra of singular integral operators with piecewise continuous coefficients on Nakano spaces (generalized Lebesgue spaces with variable exponent) with Khvedelidze…

For the algebra $\mI_1= K<x, \frac{d}{dx}, \int>$ of polynomial integro-differential operators over a field $K$ of characteristic zero, a classification of simple modules is given. It is proved that $\mI_1$ is a left and right coherent…

Contemporary presentation of the version 1 demonstrates briefly the development of our investigations and our future goals. The improved free of difficulties in interpretation and printing errors version is presented. The 256-dimensional…

The approximate representation of operators by finite matrices is analysed in terms of accuracy and convergence. The identity operator, for example, can be reconstructed using a basis of harmonic oscillator states leading to a narrow peak…

Based on direct integrals, a framework allowing to integrate a parametrised family of reproducing kernels with respect to some measure on the parameter space is developed. By pointwise integration, one obtains again a reproducing kernel…

Kernel theorems, in general, provide a convenient representation of bounded linear operators. For the operator acting on a concrete function space, this means that its action on any element of the space can be expressed as a generalised…

We present a new formula for umbral operators that yields three main insights. First, it makes explicit a connection between umbral calculus and iteration theory. Second, it leads naturally to a definition of fractional exponents of umbral…

We introduce a new class of operator algebras -- tracially complete C*-algebras -- as a vehicle for transferring ideas and results between C*-algebras and their tracial von Neumann algebra completions. We obtain structure and classification…

We discuss linear algebra of infinite-dimensional vector spaces in terms of algebraic (Hamel) bases. As an application we prove the surjectivity of a large class of linear partial differential operators with smooth ($\mathcal…

In this paper we shall focus on one-dimensional strictly local operators, the notion of which naturally arises in the context of discrete-time quantum walks on the one-dimensional integer lattice. In particular, we give an elementary…

In this contribution we analyze the spectral properties of some commonly used boundary integral operators in computational electromagnetics and of their discrete counterparts, highlighting peculiar features of their spectra. In particular,…

The well-behaved representations of the coordinate algebra of a 2-dimensional quantum complex plane are classified and a C*-algebra is defined which can be viewed as the algebra of continuous functions on the 2-dimensional quantum complex…

Spectral representations of the dilation and translation operators on $L^2({\mathbb R})$ are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions…

We use algebras of pseudodifferential operators on groupoids to study geometric operators on non-compact manifolds and singular spaces. The first step is to establish that the geometric operators are in our algebras. This then leads to…

We develop a stochastic approximation framework for learning nonlinear operators between infinite-dimensional spaces utilizing general Mercer operator-valued kernels. Our framework encompasses two key classes: (i) compact kernels, which…

Woronowicz introduced the functional calculus for normal operators in Hilbert C*-modules. The aim of this paper is to translate, if possible, some basic properties of the functional calculus in Hilbert spaces to the Hilbert C*-module…

In this paper, we study an infinite system of Fredholm series of polynomials in $\lambda$, formed, in the classical way, for a continuous Hilbert-Schmidt kernel on $\mathbb{R}\times\mathbb{R}$ of the form…