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# Search results

20 records were found.

## A dual characterization of length spaces with application to Dirichlet metric spaces

We show that under minimal assumptions, the intrinsic metric induced by a strongly local Dirichlet form induces a length space. A main input is a dual characterization of length spaces in terms of the property that the 1-Lipschitz functions form a sheaf.

## Percolation Hamiltonians

Comment: v3: final version, typos corrected; v2: references and some comments added; to appear in "Boundaries and spectra of random walks," proceedings of the Alp workshop Graz - St. Kathrein 2009, edited by D. Lenz, F. Sobieczky, W. Woess

## Delone dynamical systems and associated random operators

Comment: 19 pages; revised version

## An ergodic theorem for Delone dynamical systems and existence of the integrated density of states

Comment: 19 pages

## Generic sets in spaces of measures and generic singular continuous spectrum for Delone Hamiltonians

We show that geometric disorder leads to purely singular continuous spectrum generically. The main input is a result of Simon known as the Wonderland theorem''. Here, we provide an alternative approach and actually a slight strengthening by showing that various sets of measures defined by regularity properties are generic in the set of all measures on a locally compact metric space. As a byproduct we obtain that a generic measure on euclidean space is singular continuous.

## Spectral asymptotics of the Laplacian on supercritical bond-percolation graphs

Comment: 16 pages, typos corrected, to appear in J. Funct. Anal

## Heat kernel estimates for the $\bar\partial$-Neumann problem on $G$-manifolds

Comment: 22 pages

## Essential self-adjointness, generalized eigenforms, and spectra for the $\bar\partial$-Neumann problem on $G$-manifolds

Let $M$ be a strongly pseudoconvex complex manifold which is also the total space of a principal $G$-bundle with $G$ a Lie group and compact orbit space $\bar M/G$. Here we investigate the $\bar\partial$-Neumann Laplacian on $M$. We show that it is essentially self-adjoint on its restriction to compactly supported smooth forms. Moreover we relate its spectrum to the existence of generalized eigenforms: an energy belongs to $\sigma(\square)$ if there is a subexponentially bounded generalized eigenform for this energy. Vice versa, there is an expansion in terms of these well-behaved eigenforms so that, spectrally, almost every energy comes with such a generalized eigenform.

## The Allegretto-Piepenbrink Theorem for strongly local forms

The existence of positive weak solutions is related to spectral information on the corresponding partial differential operator.

## Eigenfunction expansion for Schrodinger operators on metric graphs

Comment: 11 pages, submitted to Jounal of Integral Equations and Operator Theory