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| Authors |
Martin Hallnäs Simon Ruijsenaars |
|---|---|
| Published in | International mathematics research notices |
| Issue | 14 |
| Pages | 4404–4449 |
| ISSN | 1073-7928 |
| Publication year | 2018 |
| Published at |
Department of Mathematical Sciences |
| Pages | 4404–4449 |
| Language | en |
| Links |
https://doi.org/10.1093/imrn/rnx020 |
| Keywords | analytic difference operators, joint eigenfunctions, relativistic Calogero-Moser systems |
| Subject categories | Mathematical Analysis, Other Mathematics |
In a previous paper we introduced and developed a recursive construction of joint eigenfunctions $J_N(a_+,a_-,b;x,y)$ 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 $J_2(b;x,y)$ and $J_3(b;x,y)$ 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 $\rE_2(b;x,y)$ and $\rE_3(b;x,y)$. In particular, we determine the dominant asymptotics for $y_1-y_2\to\infty$ and $y_1-y_2,y_2-y_3\to\infty$, resp., from which the conjectured factorized scattering can be read off.
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