✦ LIBER ✦

On spectral stability for the fractional Laplacian perturbed by unbounded obstacles

✍ Scribed by Michael Demuth; Marcel Hansmann

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 170 KB
Volume: 282
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200610819

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✦ Synopsis

Abstract

In this paper we give integral conditions for the stability of the absolutely continuous spectrum for the fractional Laplacian H~0~ = , where α ∈ (0, 2), perturbed by an unbounded obstacle Γ ⊂ R^d^ . We use the stochastic representation of the associated semigroups to derive conditions in terms of the capacity of certain subsets of Γ. In particular, obstacles with infinite capacity are allowed (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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## Abstract In this paper we show with scattering theoretical methods the absence of the singular continuous spectrum for operators that are perturbations of functions of the Laplacian. We extend the semigroup criteria developed in [9] and apply the result to the case of the fractional Laplacian (−