Volume 9, Issue 2, May 2002, Pages 181 - 209
Reflectionless Analytic Difference Operators III. Hilbert Space Aspects
Authors
S.N.M. Ruijsenaars
Corresponding Author
S.N.M. Ruijsenaars
Received 15 November 2001, Accepted 12 March 2002, Available Online 1 May 2002.
- DOI
- 10.2991/jnmp.2002.9.2.4How to use a DOI?
- Abstract
In the previous two parts of this series of papers, we introduced and studied a large class of analytic difference operators admitting reflectionless eigenfunctions, focusing on algebraic and function-theoretic features in the first part, and on connections with solitons in the second one. In this third part we study our difference operators from a quantum mechanical viewpoint. We show in particular that for an arbitrary diference operator A from a certain subclass, the reflectionless A-eigenfunctions can be used to construct an unbounded self-adjoint reflectionless operator  on L2 (R, dx), whose action on a suitable core coincides with that of A.
- 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/).
Cite this article
TY - JOUR AU - S.N.M. Ruijsenaars PY - 2002 DA - 2002/05/01 TI - Reflectionless Analytic Difference Operators III. Hilbert Space Aspects JO - Journal of Nonlinear Mathematical Physics SP - 181 EP - 209 VL - 9 IS - 2 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.2002.9.2.4 DO - 10.2991/jnmp.2002.9.2.4 ID - Ruijsenaars2002 ER -