Home > Research > Publications & Outputs > Decay rates at infinity for solutions to period...

Electronic data

  • EllDecRSErev

    Rights statement: 6m

    Accepted author manuscript, 331 KB, PDF document

    Embargo ends: 1/01/50

    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License


Text available via DOI:

View graph of relations

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


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.