We study Hilbert space aspects of explicit eigenfunctions for analytic difference operators that arise in the context of relativistic two-particle Calogero–Moser systems. We restrict attention to integer coupling constants g/ℏ, for which no reflection occurs. It is proved that the eigenfunction transforms are isometric, provided a certain dimensionless parameter a varies over a bounded interval (0,_a_max), whereas isometry is shown to be violated for generic a larger than _a_max. The anomaly is encoded in an explicit finite-rank operator, whose rank increases to ∞ as a goes to ∞.
Cite this article
Simon N. M. Ruijsenaars, Hilbert Space Theory for Reflectionless Relativistic Potentials. Publ. Res. Inst. Math. Sci. 36 (2000), no. 6, pp. 707–753DOI 10.2977/PRIMS/1195139643