Stability of Singular Spectral Types under Decaying Perturbations

Details Stability of Singular Spectral Types under Decaying Perturbations Stability of Singular Spectral Types under Decaying Perturbations

2001-10-13

arxiv.org/abs/math/0110139v1

Mathematics

Spectral Theory

25 pages

Scientific paper

We look at invariance of a.e. boundary condition spectral behavior under
perturbations, $W$, of half-line, continuum or discrete Schr\"odinger
operators. We extend the results of del Rio, Simon, Stolz from compactly
supported $W$'s to suitable short-range $W$. We also discuss invariance of the
local Hausdorff dimension of spectral measures under such perturbations.

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