Isometric Reflectionless Eigenfunction Transforms for Higher-order AOs

DOI

10.2991/jnmp.2005.12.s1.45How to use a DOI?

Abstract

In a previous paper (Regular and Chaotic Dynamics 7 (2002), 351­391, Ref. [1]), we obtained various results concerning reflectionless Hilbert space transforms arising from a general Cauchy system. Here we extend these results, proving in particular an isometry property conjectured in Ref. [1]. Crucial input for the proof comes from previous work on a special class of relativistic Calogero-Moser systems. Specifically, we exploit results on action-angle maps for the pertinent systems and their relation to the 2D Toda soliton tau-functions. The reflectionless transforms may be viewed as eigenfunction transforms for an algebra of higher-order analytic difference operators.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - S.N.M. Ruijsenaars
PY  - 2005
DA  - 2005/01/01
TI  - Isometric Reflectionless Eigenfunction Transforms for Higher-order AOs
JO  - Journal of Nonlinear Mathematical Physics
SP  - 565
EP  - 598
VL  - 12
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.s1.45
DO  - 10.2991/jnmp.2005.12.s1.45
ID  - Ruijsenaars2005
ER  -