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  • EllDecRSErev

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Decay rates at infinity for solutions to periodic Schrödinger equations

Research output: Contribution to journalJournal article

E-pub ahead of print
<mark>Journal publication date</mark>30/01/2019
<mark>Journal</mark>Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Number of pages13
Publication statusE-pub ahead of print
Early online date30/01/19
Original languageEnglish

Abstract

We consider the equation ∆u = Vu in the half-space 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 ∆u = Vu is studied as part of a broader class of elliptic evolution equations.