Related papers: A quasi-interpolation operator yielding fully comp…
The present paper is devoted to the boundedness of fractional integral operators in Morrey spaces defined on quasimetric measure spaces. In particular, Sobolev, trace and weighted inequalities with power weights for potential operators are…
Finite rank perturbations of a semi-bounded self-adjoint operator A are studied in the scale of Hilbert spaces associated with A. A concept of quasi-boundary value space is used to describe self-adjoint operator realizations of regular and…
We study the proximity operator of the nonconvex, scale-invariant ratio $h(\vx)=\|\vx\|_{1}/\|\vx\|_{2}$ and show it can be computed exactly in any dimension. By expressing $\vx=r\vu$ and exploiting sign and permutation invariance, we…
This paper analyzes the approximation properties of spaces of piece-wise tensor product polynomials over box meshes with a focus on application to IsoGeometric Analysis (IGA). The errors are measured in Lebesgue norms. Estimates of…
The purpose of this paper is to discuss the construction of a linear operator, referred to as the bubble transform, which maps scalar functions defined on a bounded domain $\Omega$ in $\mathbb{R}^n$ into a collection of functions with local…
Given gridded cell-average data of a smooth multivariate function, we present a constructive explicit procedure for generating a high-order global approximation of the function. One contribution is the derivation of high order…
We study multivariate numerical integration of smooth functions in weighted Sobolev spaces with dominating mixed smoothness $\alpha\geq 2$ defined over the $s$-dimensional unit cube. We propose a new quasi-Monte Carlo (QMC)-based quadrature…
We consider the fractional Schr\"odinger operator with Hardy potential and critical or subcritical coupling constant. This operator generates a natural scale of homogeneous Sobolev spaces which we compare with the ordinary homogeneous…
The residual finite-dimensionality of a $\mathrm{C}^*$-algebra is known to be encoded in a topological property of its space of representations, stating that finite-dimensional representations should be dense therein. We extend this…
Hardware implementations of complex functions regularly deploy piecewise polynomial approximations. This work determines the complete design space of piecewise polynomial approximations meeting a given accuracy specification. Knowledge of…
This paper investigates the asymptotic convergence behavior of high-order proximal-point algorithms (HiPPA) toward global minimizers, extending the analysis beyond sublinear convergence rate results. Specifically, we consider the proximal…
We study strongly measurable random bounded operators on separable Hilbert spaces and analyze two simple iterations driven by independent random positive contractions. The first, a Kaczmarz-like iteration, converges in mean square and…
We construct $\Delta$-operators $F[\Delta]$ on the space of almost symmetric functions $\mathscr{P}_{as}^{+}$. These operators extend the usual $\Delta$-operators on the space of symmetric functions $\Lambda \subset \mathscr{P}_{as}^{+}$…
Histopolation, or interpolation on segments, is a mathematical technique used to approximate a function $f$ over a given interval $I=[a,b]$ by exploiting integral information over a set of subintervals of $I$. Unlike classical polynomial…
This paper is a continuation to the study of generalized quasi contractive operators, essentially due to Akhtar et al. [A multi-step implicit iterative process for common fixed points of generalized C^{q}-operators in convex metric spaces,…
In this paper, we aim to introduce and characterize the concept of numerical radius orthogonality of operators on a complex Hilbert space $\mathcal{H}$ which are bounded with respect to the semi-norm induced by a positive operator $A$ on…
For compact self-adjoint operators in Hilbert spaces, two algorithms are proposed to provide fully computable a posteriori error estimate for eigenfunction approximation. Both algorithms apply well to the case of tight clusters and multiple…
We show that a partition of the unity (or POVM) on a Hilbert space that is almost orthogonal is close to an orthogonal POVM in the same von Neumann algebra. This generalizes to infinite dimension previous results in matrix algebras by…
The quasicontinuum approximation is a method to reduce the atomistic degrees of freedom of a crystalline solid by piecewise linear interpolation from representative atoms that are nodes for a finite element triangulation. In regions of the…
Two necessary and sufficient conditions for an operator to be semi-normal are revealed. For a Volterra integration operator the set where the operator and its adjoint are metrically equal is described.