Journal of Nonlinear Mathematical Physics

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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
9 - 2
Pages
181 - 209
Publication Date
2002/05/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.2991/jnmp.2002.9.2.4How to use a DOI?
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  -