7 papers
Convergence of Schrödinger operators on domains with scaled resonant potentials
Vladimir Lotoreichik, Olaf Post
We consider Schrödinger operators on a bounded, smooth domain of dimension with Dirichlet boundary conditions and a properly scaled potential, which depends only on the…
First order operators on shrinking graph-like spaces
Pavel Exner, Olaf Post
In this article we discuss the convergence of first order operators on a thickened graph (a graph-like space) towards a similar operator on the underlying metric graph. On the grap…
A distance between operators acting in different Hilbert spaces and operator convergence
Olaf Post, Jan Simmer
The aim of the present article is to give an introduction to the concept of quasi-unitary equivalence and to define several (pseudo-)metrics on the space of self-adjoint operators…
Quasi-unitary equivalence and generalised norm resolvent convergence
Olaf Post, Jan Simmer
The purpose of this article is to give a short introduction to the concept of quasi-unitary equivalence of quadratic forms and its consequences. In particular, we improve an estima…
Manifolds with many small wormholes: norm resolvent and spectral convergence
Colette Anné, Olaf Post
We present results concerning the norm convergence of resolvents for wildperturbations of the Laplace-Beltrami operator. This article is a continuation of ouranalysis on wildly per…
Distances between operators acting on different Hilbert spaces
Olaf Post, Sebastian Zimmer
The aim of this article is to define and compare several distances (or metrics) between operators acting on different (separable) Hilbert spaces. We consider here three main cases…