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- Title
Joint Eigenfunctions for the Relativistic Calogero–Moser Hamiltonians of Hyperbolic Type: I. First Steps.
- Authors
Hallnäs, Martin; Ruijsenaars, Simon
- Abstract
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.
- Subjects
EIGENFUNCTIONS; RELATIVISTIC theorems (Relativity); HAMILTONIAN systems; HYPERBOLIC functions; RECURSION theory; DIFFERENCE operators
- Publication
IMRN: International Mathematics Research Notices, 2014, Vol 2014, Issue 16, p4400
- ISSN
1073-7928
- Publication type
Article
- DOI
10.1093/imrn/rnt076