Joint eigenfunctions for the relativistic Calogero-Moser Hamiltonians of hyperbolic type: I. First steps.

2014-07-21T13:41:57Z (GMT) by Martin Hallnas Simon Ruijsenaars
We present and develop a recursion scheme to construct joint eigenfunctions for the commuting analytic difference operators associated with the integrable N-particle systems of hyperbolic relativistic Calogero-Moser type. The scheme is based on kernel identities we obtained in previous work. In this first paper of a series we present the formal features of the scheme, show explicitly its arbitrary-N viability for the `free' cases, and supply the analytic tools to prove the joint eigenfunction properties in suitable holomorphy domains.