Related papers: Convergence of operator-semigroups associated with…

For smooth bounded open sets in euclidean space, we construct corresponding contractive linear extension operators for the space of continuous functions which preserve regularity of functions in the domain of the Robin Laplacian. We also…

The paper is devoted to the investigation of Segal's entropy in semifinite von Neumann algebras. The following questions are dealt with: semicontinuity, the 'ideal-like' structure of the linear span of the set of operators with finite…

We consider generalizations of Dunkl's differential-difference operators associated with groups generated by reflections. The commutativity condition is equivalent to certain functional equations. These equations are solved in many cases.…

We consider a family of compact manifolds which shrinks with respect to an appropriate parameter to a graph. The main result is that the spectrum of the Laplace-Beltrami operator converges to the spectrum of the (differential) Laplacian on…

We identify the norm of the semigroup generated by the non-self-adjoint harmonic oscillator acting on $L^2(\Bbb{R})$, for all complex times where it is bounded. We relate this problem to embeddings between Gaussian-weighted spaces of…

The first our aim is to clarify the results obtained by Lidskii devoted to the decomposition on the root vector system of the non-selfadjoint operator. We use a technique of the entire function theory and introduce a so-called Schatten-von…

We consider a bounded connected open set $\Omega \subset {\rm R}^d$ whose boundary $\Gamma$ has a finite $(d-1)$-dimensional Hausdorff measure. Then we define the Dirichlet-to-Neumann operator $D_0$ on $L_2(\Gamma)$ by form methods. The…

We study uniform Lipschitz regularity estimates for elliptic systems in divergence form with continuous coefficients, based on rapidly oscillating periodic coefficients derived from homogenization theory. We extend a result by Avellaneda…

We establish optimal L^p bounds for the nontangential maximal function of the gradient of the solution to a second order elliptic operator in divergence form, possibly non-symmetric, with bounded measurable coefficients independent of the…

A semiregular operator on a Hilbert C^*-module, or equivalently, on the C^*-algebra of `compact' operators on it, is a closable densely defined operator whose adjoint is also densely defined. It is shown that for operators on extensions of…

The purpose of this paper is to revisit the proof of the Gearhart-Pr\"uss-Huang-Greiner theorem for a semigroup $S(t)$, following the general idea of the proofs that we have seen in the literature and to get an explicit estimate on the…

We present some properties of orthogonality and relate them with support disjoint and norm inequalities in p Schatten ideals. In addition, we investigate the problem of characterization of norm parallelism for bounded linear operators. We…

Truncated Toeplitz operators in a model space are C--symmetric with respect to a natural conjugation in that space. We show that this and another conjugation associated to an orthogonal decomposition possess unique properties and we study…

We prove sufficient conditions for Hausdorff convergence of the spectra of sequences of closed operators defined on varying Hilbert spaces and converging in norm-resolvent sense, i.e. $\|J_\varepsilon(1+A_\varepsilon)^{-1} -…

This chapter deals with the notion of the resolvent of a self-adjoint operator. We pay special attention to the convergence of unbounded self-adjoint operators in several resolvent senses, and how they are related to the convergence of…

We prove a generalization of the orthogonality relations of Duflo and Moore for ergodic, trace-preserving group actions on von Neumann algebras that are integrable in a suitable sense. We also obtain convolution inequalities that generalize…

We establish spectral convergence results of approximations of unbounded non-selfadjoint linear operators with compact resolvents by operators that converge in generalized strong resolvent sense. The aim is to establish general assumptions…

We establish a Talenti-type symmetrization result in the form of mass concentration (i.e. integral comparison) for very general linear nonlocal elliptic problems, equipped with homogeneous Dirichlet boundary conditions. In this framework,…

The technique of Caffarelli and Silvestre, characterizing the fractional Laplacian as the Dirichlet-to-Neumann map for a function U satisfying an elliptic equation in the upper half space with one extra spatial dimension, is shown to hold…

In this paper, we introduce compatible ternary Leibniz algebras, (dual)Nijenhuis pairs from the second-order deformation of ternary Leibniz algebras with a representarion and study the invariance of certains operators (generalized…