Decay rates at infinity for solutions to periodic Schrödinger equations
Daniel M. Elton · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 2019
Abstract We consider the equation Δu = Vu in the half-space ${\open R}_ + ^d $ , d ⩾ 2 where V has certain periodicity properties. In particular, we show that such equations cannot have non-trivial superexponentially decaying solutions. As an application this leads to a new proof for the absolute continuity of the spectrum of particular periodic Schrödinger operators. The equation Δu = Vu is studied as part of a broader class of elliptic evolution equations.