Joint Eigenfunctions for the Relativistic Calogero–Moser Hamiltonians of Hyperbolic Type: I. First Steps

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.