singularly continuous spectrum
Springer Online Journal Archives 1860-2000
Abstract Let H be a semibounded perturbation of the Laplacian H 0 in L 2(ℝ d ). For an admissible function ϕ sufficient conditions are given for the completeness of the scattering system ϕ(H), ϕ(H 0). If ϕ is the exponential function and if e− λ H is an integral operator we denote the kernel of the difference D λ = e− λ H − e− λ H 0 by D λ(x, y), λ 〉 0. The singularly continuous spectrum of H is empty if ∫ℝd dx ∫ℝ d 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.
Type of Medium: