Related papers: Equiconvergence theorems for differential operator…

For an arbitrary operator A on a Banach space X which is a generator of C_0-group with certain growth condition at the infinity, the direct theorems on connection between the smoothness degree of a vector $x\in X$ with respect to the…

We consider weighted uniform convergence of entire analogues of the Gr\"unwald operator on the real line. The main result deals with convergence of entire interpolations of exponential type $\tau>0$ at zeros of Bessel functions in spaces…

For several different boundary conditions (Dirichlet, Neumann, Robin), we prove norm-resolvent convergence for the operator $-\Delta$ in the perforated domain $\Omega\setminus \bigcup_{ i\in 2\varepsilon\mathbb Z^d }B_{a_\varepsilon}(i),$…

We introduce a simple, general, and convergent scheme to compute generalized eigenfunctions of self-adjoint operators with continuous spectra on rigged Hilbert spaces. Our approach does not require prior knowledge about the eigenfunctions,…

We present new conditions for semigroups of positive operators to converge strongly as time tends to infinity. Our proofs are based on a novel approach combining the well-known splitting theorem by Jacobs, de Leeuw and Glicksberg with a…

We prove a new duality theorem for the category of precontact algebras which implies the Stone Duality Theorem, its connected version obtained in arXiv:1508.02220v3, 1-44 (to appear in Topology Appl.), the recent duality theorems of…

We study a homogenization question for stochastic divergence type operator

General stochastic Euler schemes for ordinary differential equations are studied. We give proofs on the consistency, the rate of convergence and the asymptotic normality of these procedures.

In this paper, we give direct theorems on point wise and global approximation by new variants of Bernstein-Durrmeyer operator, introduced by A.-M. et al.[1].

We provide a new version of the well-known Birkhoff-Kellogg invariant-direction Theorem in product spaces. Our results concern operator systems and give the existence of component-wise eigenvalues, instead of scalar eigenvalues as in the…

In this work, we characterise the statistics of Markov chains by constructing an associated sequence of periodic differential operators. Studying the density of states of these operators reveals the absolutely continuous invariant measure…

In the present paper, we propose to give an extension to the context of Dunkl theory of the notion of translation and in connection with this a corresponding extension of Taylor's formula. More precisely, we prove some properties and…

The basic results for nonlinear operators are given. These results include nonlinear versions of classical uniform boundedness theorem and Hahn-Banach theorem. Furthermore, the mappings from a metrizable space into another normed space can…

Convergence of non-uniform spherical averages is obtained for measure-preserving actions of free groups. This result generalizes theorems of Grigorichuk, Nevo and Stein [in particular, a simpler proof of the Nevo-Stein theorem about uniform…

In this paper, we consider the polynomial and exponential convergence rate of weighted Birkhoff averages of irrational rotations on tori. It is shown that these can be achieved for finite and infinite dimensional tori which correspond to…

This paper has two purposes. First, we show that the classical Stein-Weiss inequality is true for p=1. Second, by considering a family of strong fractional integral operators whose kernels have singularity on every coordinate subspace, we…

For a Dunford-Schwartz operator in a fully symmetric space of measurable functions of an arbitrary measure space, we prove pointwise convergence of the conventional and weighted ergodic averages.

We introduce a suitable notion of integral operators (comprising the fractional Laplacian as a particular case) acting on functions with minimal requirements at infinity. For these functions, the classical definition would lead to divergent…

We present a new and simple approach to the theory of multiple operator integrals that applies to unbounded operators affiliated with general von Neumann algebras. For semifinite von Neumann algebras we give applications to the Fr\'echet…

We establish distributional estimates for noncommutative martingales, in the sense of decreasing rearrangements of the spectra of unbounded operators, which generalises the study of distributions of random variables. Our results include…