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  • EllDecRSErev

    Rights statement: https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/decay-rates-at-infinity-for-solutions-to-periodic-schrodinger-equations/D4D25C3E296668E6FEE2D8E4FB8FD06C The final, definitive version of this article has been published in the Journal, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 150 (3), pp 1113-1126 2020, © 2020 Cambridge University Press.

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Decay rates at infinity for solutions to periodic Schrödinger equations

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published
<mark>Journal publication date</mark>1/06/2020
<mark>Journal</mark>Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Issue number3
Volume150
Number of pages14
Pages (from-to)1113-1126
Publication StatusPublished
Early online date30/01/19
<mark>Original language</mark>English

Abstract

We consider the equation ∆u = Vu in the half-space Rd+ , 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.

Bibliographic note

https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/decay-rates-at-infinity-for-solutions-to-periodic-schrodinger-equations/D4D25C3E296668E6FEE2D8E4FB8FD06C The final, definitive version of this article has been published in the Journal, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 150 (3), pp 1113-1126 2020, © 2020 Cambridge University Press.