✦ LIBER ✦

Asymptotic completeness for functions of the Laplacian perturbed by potentials and obstacles

✍ Scribed by Eckhard Giere

Publisher: John Wiley and Sons
Year: 2004
Tongue: English
Weight: 278 KB
Volume: 263-264
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.200310127

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✦ Synopsis

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 (−Δ)^α/2^ where α ∈ (0, 2). We prove weighted L^p^ estimates for the semigroups generated by H~0~ = (−Δ)^α/2^ and H~0~ + V . These estimates are used for the verification of the semigroup criteria. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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