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

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## 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:

?? mathematics(all) ??

Departments:

ID Code:

88785

Deposited By:

Deposited On:

20 Nov 2017 12:48

Refereed?:

Yes

Published?:

Published

Last Modified:

31 Jan 2024 00:30