# Joint Eigenfunctions for the Relativistic Calogero–Moser Hamiltonians of Hyperbolic Type. III. Factorized Asymptotics

@article{Hallnas2019JointEF,
title={Joint Eigenfunctions for the Relativistic Calogero–Moser Hamiltonians of Hyperbolic Type. III. Factorized Asymptotics},
author={Martin A. Hallnas and Simon Ruijsenaars},
journal={International Mathematics Research Notices},
year={2019}
}
• Published 30 May 2019
• Mathematics
• International Mathematics Research Notices
In the two preceding parts of this series of papers, we introduced and studied a recursion scheme for constructing joint eigenfunctions $J_N(a_+, a_-,b;x,y)$ of the Hamiltonians arising in the integrable $N$-particle systems of hyperbolic relativistic Calogero–Moser type. We focused on the 1st steps of the scheme in Part I and on the cases $N=2$ and $N=3$ in Part II. In this paper, we determine the dominant asymptotics of a similarity-transformed function $\textrm{E}_N(b;x,y)$ for $y_j-y_{j+1… 3 Citations • Mathematics Communications in Mathematical Physics • 2022 We present a perturbative construction of two kinds of eigenfunctions of the commuting family of difference operators defining the elliptic Ruijsenaars system. The first kind corresponds to elliptic • Mathematics Communications in Mathematical Physics • 2021 The super-Macdonald polynomials, introduced by Sergeev and Veselov (Commun Math Phys 288: 653–675, 2009), generalise the Macdonald polynomials to (arbitrary numbers of) two kinds of variables, and • Mathematics • 2020 For any variable number, a non-stationary Ruijsenaars function was recently introduced as a natural generalization of an explicitly known asymptotically free solution of the trigonometric Ruijsenaars ## References SHOWING 1-10 OF 17 REFERENCES • Mathematics • 2016 In a previous paper we introduced and developed a recursive construction of joint eigenfunctions$J_N(a_+,a_-,b;x,y)\$ for the Hamiltonians of the hyperbolic relativistic Calogero-Moser system with
In previous work we introduced and studied a function R(a+;a ;c;v; ^) that is a generalization of the hypergeometric function 2F1 and the Askey{Wilson polynomials. When the coupling vector c 2 C 4 is
• Physics
• 2015
We present and study a novel class of one-dimensional Hilbert space eigenfunction transforms that diagonalize analytic difference operators encoding the (reduced) two-particle relativistic hyperbolic
Poincaré-invariant generalizations of the Galilei-invariant Calogero-MoserN-particle systems are studied. A quantization of the classical integralsS1, ...,SN is presented such that the operatorsŜ1,
• Mathematics
• 2014
We develop basic constructions of the Baxter operator formalism for the Macdonald polynomials associated with root systems of type A. Precisely, we construct a bispectral pair of mutually commuting
We survey results on Galilei-and Poincare-invariant CalogeroMoser and Toda N-particle systems, both in the context of classical mechanics and of quantum mechanics. Special attention is given to