On the Spectra of Real and Complex Lamé Operators
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On the Spectra of Real and Complex Lamé Operators
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| Creator |
Haese-Hill, W.A.
Hallnäs, M.A. Veselov, A.P. |
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| Description |
We study Lamé operators of the form L=−d²/dx²+m(m+1)ω²℘(ωx+z₀), with m∈N and ω a half-period of ℘(z). For rectangular period lattices, we can choose ω and z0 such that the potential is real, periodic and regular. It is known after Ince that the spectrum of the corresponding Lamé operator has a band structure with not more than m gaps. In the first part of the paper, we prove that the opened gaps are precisely the first m ones. In the second part, we study the Lamé spectrum for a generic period lattice when the potential is complex-valued. We concentrate on the m=1 case, when the spectrum consists of two regular analytic arcs, one of which extends to infinity, and briefly discuss the m=2 case, paying particular attention to the rhombic lattices. |
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| Date |
2019-02-18T16:10:46Z
2019-02-18T16:10:46Z 2017 |
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| Type |
Article
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| Identifier |
On the Spectra of Real and Complex Lamé Operators
/ W.A. Haese-Hill, M.A. Hallnäs, A.P. Veselov // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 32 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 34L40; 47A10; 33E10 DOI:10.3842/SIGMA.2017.049 http://dspace.nbuv.gov.ua/handle/123456789/148577 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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