Decay rates at infinity for solutions to periodic Schrödinger equations

Elton, Daniel Mark (2020) Decay rates at infinity for solutions to periodic Schrödinger equations. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 150 (3). pp. 1113-1126. ISSN 0308-2105

[img]
Preview
PDF (EllDecRSErev)
EllDecRSErev.pdf - Accepted Version
Available under License Creative Commons Attribution-NonCommercial.

Download (339kB)

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.

Item Type:
Journal Article
Journal or Publication Title:
Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Additional Information:
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.
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
88785
Deposited By:
Deposited On:
20 Nov 2017 12:48
Refereed?:
Yes
Published?:
Published
Last Modified:
18 Sep 2020 03:50