Schrödinger operators with empty singularly continuous spectra

Demuth, Michael ; Sinha, Kalyan B. (1999) Schrödinger operators with empty singularly continuous spectra Mathematical Physics, Analysis and Geometry, 2 (3). pp. 223-244. ISSN 1385-0172

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Let H be a semibounded perturbation of the Laplacian H0 in L2(Rd). For an admissible function φ sufficient conditions are given for the completeness of the scattering system {φ(H), φ(H0). If φ is the exponential function and if e−λ H is an integral operator we denote the kernel of the difference Dλ= e−λ H − e−λ H0 by Dλ(x, y), λ> 0. The singularly continuous spectrum of H is empty if ∫Rd dx ∫Rd dy |Dλ(x,y)| (1+ |y|2)α< ∞ for some α > 1. This result is applied to potential perturbations and to perturbations by imposing Dirichlet boundary conditions.

Item Type:Article
Source:Copyright of this article belongs to Springer.
Keywords:Singularly Continuous Spectrum; Schrödinger Operators; Obstacle Scattering
ID Code:80972
Deposited On:02 Feb 2012 14:12
Last Modified:02 Feb 2012 14:12

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