Hilbert-Schmidt Operators vs. Integrable Systems of Elliptic Calogero-Moser Type III. The Heun Case
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Hilbert-Schmidt Operators vs. Integrable Systems of Elliptic Calogero-Moser Type III. The Heun Case
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| Creator |
Ruijsenaars, Simon N.M.
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| Description |
The Heun equation can be rewritten as an eigenvalue equation for an ordinary differential operator of the form −d²/dx²+V(g;x), where the potential is an elliptic function depending on a coupling vector g ∈ R⁴. Alternatively, this operator arises from the BC1 specialization of the BCN elliptic nonrelativistic Calogero-Moser system (a.k.a. the Inozemtsev system). Under suitable restrictions on the elliptic periods and on g, we associate to this operator a self-adjoint operator H(g) on the Hilbert space H = L²([0,ω₁],dx), where 2ω₁ is the real period of V(g;x). For this association and a further analysis of H(g), a certain Hilbert-Schmidt operator I(g) on H plays a critical role. In particular, using the intimate relation of H(g) and I(g), we obtain a remarkable spectral invariance: In terms of a coupling vector c ∈ R⁴ that depends linearly on g, the spectrum of H(g(c)) is invariant under arbitrary permutations σ(c), σ ∈ S₄.
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| Date |
2019-02-19T17:47:23Z
2019-02-19T17:47:23Z 2009 |
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| Type |
Article
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| Identifier |
Hilbert-Schmidt Operators vs. Integrable Systems of Elliptic Calogero-Moser Type III. The Heun Case / Simon N.M. Ruijsenaars // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 20 назв. — англ.
1815-0659 2000 Mathematics Subject Classification: 33E05; 33E10; 46N50; 81Q05; 81Q10 http://dspace.nbuv.gov.ua/handle/123456789/149153 |
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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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