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    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

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Decay rates at infinity for solutions to periodic Schrödinger equations. / Elton, Daniel Mark.
In: Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 150, No. 3, 01.06.2020, p. 1113-1126.

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

Harvard

Elton, DM 2020, 'Decay rates at infinity for solutions to periodic Schrödinger equations', Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol. 150, no. 3, pp. 1113-1126. https://doi.org/10.1017/prm.2018.87

APA

Elton, D. M. (2020). Decay rates at infinity for solutions to periodic Schrödinger equations. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 150(3), 1113-1126. https://doi.org/10.1017/prm.2018.87

Vancouver

Elton DM. Decay rates at infinity for solutions to periodic Schrödinger equations. Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 2020 Jun 1;150(3):1113-1126. Epub 2019 Jan 30. doi: 10.1017/prm.2018.87

Author

Elton, Daniel Mark. / Decay rates at infinity for solutions to periodic Schrödinger equations. In: Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 2020 ; Vol. 150, No. 3. pp. 1113-1126.

Bibtex

@article{a96cfbd3f2ea49d284076891b522c1b1,
title = "Decay rates at infinity for solutions to periodic Schr{\"o}dinger equations",
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 Schr{\"o}dinger operators. The equation ∆u = Vu is studied as part of a broader class of elliptic evolution equations.",
author = "Elton, {Daniel Mark}",
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, {\textcopyright} 2020 Cambridge University Press. ",
year = "2020",
month = jun,
day = "1",
doi = "10.1017/prm.2018.87",
language = "English",
volume = "150",
pages = "1113--1126",
journal = "Proceedings of the Royal Society of Edinburgh: Section A Mathematics",
issn = "0308-2105",
publisher = "Cambridge University Press",
number = "3",

}

RIS

TY - JOUR

T1 - Decay rates at infinity for solutions to periodic Schrödinger equations

AU - Elton, Daniel Mark

N1 - 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.

PY - 2020/6/1

Y1 - 2020/6/1

N2 - 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.

AB - 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.

U2 - 10.1017/prm.2018.87

DO - 10.1017/prm.2018.87

M3 - Journal article

VL - 150

SP - 1113

EP - 1126

JO - Proceedings of the Royal Society of Edinburgh: Section A Mathematics

JF - Proceedings of the Royal Society of Edinburgh: Section A Mathematics

SN - 0308-2105

IS - 3

ER -