Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 4th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 6–15, 2002. Sofia: Coral Press Scientific Publishing (ISBN 954-90618-4-1/pbk). 296-302 (2003).
The authors consider a difference -analogue of the dressing chain and prove the following theorem: Suppose is even, are positive, and . Then the system
has an -parametric family of solutions. The operator is bounded for each and its spectrum is discrete and is contained in the interval . It can be found by using the Darboux scheme,
For each , the eigenfunctions of the operator can also be obtained by using the Darboux scheme,
and these eigenfunctions form a complete family in