We investigate the Schro dinger operator H=&2+V acting in L 2 (R n ), n 2, for potentials V that satisfy : x V(x)=O(|x| &|:| ) as |x| Ä . By introducing coordinates on R n closely related to a relevant eikonal equation we obtain an eigenfunction expansion for H at high energies.
Zero-measure Cantor spectrum for Schrödinger operators with low-complexity potentials
✍ Scribed by David Damanik; Daniel Lenz
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 190 KB
- Volume
- 85
- Category
- Article
- ISSN
- 0021-7824
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📜 SIMILAR VOLUMES
We prove a strong unique continuation result for Schrödinger inequalities, i.e., we obtain that a flat \(u\) so that \(|\Delta u| \leqslant|V u|\) should be zero, provided that \(V\) is a radial Kato potential. It gives an extension of a result by E. B. Fabes, N. Garofalo and F. H. Lin [3] who got a
## Abstract We show that when a potential __b~n~__ of a discrete Schrödinger operator, defined on __l__^2^(ℤ^+^), slowly oscillates satisfying the conditions __b~n~__ ∈ __l__^∞^ and ∂__b~n~__ = __b__~__n__ +1~ – __b~n~__ ∈ __l^p^__, __p__ < 2, then all solutions of the equation __Ju__ = __Eu__ are