Geodesic
Self-Adjoint A$\Delta$Os with Vanishing Reflection
Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 1, pp. 116-132 
S. Ruijsenaars. Self-Adjoint A$\Delta$Os with Vanishing Reflection. Teoretičeskaâ i matematičeskaâ fizika, Tome 128 (2001) no. 1, pp. 116-132. http://geodesic.mathdoc.fr/item/TMF_2001_128_1_a9/
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     title = {Self-Adjoint {A}$\Delta${Os} with {Vanishing} {Reflection}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

We review our work concerning ordinary linear second-order analytic difference operators (A$\Delta$Os) that admit reflectionless eigenfunctions. This operator class is far more extensive than the reflectionless Schrödinger and Jacobi operators corresponding to KdV and Toda lattice solitons. A subclass of reflectionless A$\Delta$Os, which generalizes the latter class of differential and discrete difference operators, is shown to correspond to the soliton solutions of a nonlocal Toda-type evolution equation. Further restrictions give rise to A$\Delta$Os with isometric eigenfunction transformations, which can be used to associate self-adjoint operators on $L^2(\mathbb R,dx)$ with the A$\Delta$Os.

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