Hallnas, M and Ruijsenaars, S (2018) Joint eigenfunctions for the relativistic Calogero-Moser Hamiltonians of hyperbolic type. II. The two- and three-variable cases. International Mathematics Research Notices, 2018 (14). pp. 4404-4409. ISSN 1073-7928
Abstract
In a previous paper we introduced and developed a recursive construction of joint eigenfunctions JN (a+₊, a−, b; x, y) for the Hamiltonians of the hyperbolic relativistic Calogero-Moser system with arbitrary particle number N. In this paper we focus on the cases N = 2 and N = 3, and establish a number of conjectured features of the corresponding joint
eigenfunctions. More specifically, choosing a+, a− positive, we prove that J₂(b; x, y) and J₃(b; x, y) extend to globally meromorphic functions that satisfy various invariance properties as well as a duality relation. We also obtain detailed information on the asymptotic behavior of similarity transformed functions E₂(b; x, y) and E₃(b; x, y). In particular, we
determine the dominant asymptotics for y₁ − y₂ → ∞ and y₁ − y₂, y₂ − y₃ → ∞, resp., from which the conjectured factorized scattering can be read off.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2017. Published by Oxford University Press. This is a pre-copyedited, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record, Martin Hallnäs, Simon Ruijsenaars; Joint Eigenfunctions for the Relativistic Calogero–Moser Hamiltonians of Hyperbolic Type II. The Two- and Three-Variable Cases. Int Math Res Notices 2017, rnx020, is available online at: https://doi.org/10.1093/imrn/rnx020. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 26 Jan 2017 10:20 |
Last Modified: | 28 Sep 2018 13:03 |
Published Version: | https://doi.org/10.1093/imrn/rnx020 |
Status: | Published |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/imrn/rnx020 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:111202 |