We prove exponential localization at all energies for one-dimensional continuous Anderson-type models with single site potentials of changing sign. A periodic background potential is allowed. The main problem arises from non-monotonicity; i.e., the operator does not depend monotonically in the form
Regularization of the non-stationary Schrödinger operator
✍ Scribed by Paula Cerejeiras; Nelson Vieira
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 179 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.1050
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✦ Synopsis
Abstract
In this paper we prove a L~p~‐decomposition where one of the components is the kernel of a first‐order differential operator that factorizes the non‐stationary Schrödinger operator −Δ−i∂~t~. Copyright © 2008 John Wiley & Sons, Ltd.
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