On the absolute continuity of Schrödinger operators with spherically symmetric, long-range potentials, I

Absolutely continuous spectrum of discre

Absolutely continuous spectrum of discrete Schrödinger operators with slowly oscillating potentials

✍ Ahyoung Kim; Alexander Kiselev 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 220 KB

## 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