Hilbert Space Theory for Reflectionless Relativistic Potentials
Simon N. M. Ruijsenaars
Centre for Mathematics and Computer Science, Amsterdam, Netherlands
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Abstract
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 , for which no reflection occurs. It is proved that the eigenfunction transforms are isometric, provided a certain dimensionless parameter varies over a bounded interval , whereas isometry is shown to be violated for generic larger than . The anomaly is encoded in an explicit finite-rank operator, whose rank increases to as 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. 707–753
DOI 10.2977/PRIMS/1195139643