Joint eigenfunctions for the relativistic Calogero-Moser Hamiltonians of hyperbolic type: I. First steps. Martin Hallnas Simon Ruijsenaars 2134/15265 https://repository.lboro.ac.uk/articles/journal_contribution/Joint_eigenfunctions_for_the_relativistic_Calogero-Moser_Hamiltonians_of_hyperbolic_type_I_First_steps_/9376790 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. 2014-07-21 13:41:57 untagged Mathematical Sciences not elsewhere classified