We consider the class of reflectionless Sturm-Liouville potentials and the subclass consisting of "Sato-Segal-Wilson" potentials. We construct illustrative examples lying in these classes, in particular we adapt the constructions of Craig and Levitan to the Sturm-Liouville case. We also discuss an inverse problem of Kotani type in the context of Sato-Segal-Wilson potentials.
Some remarks concerning reflectionless Sturm-Liouville potentials / R. Johnson; L. Zampogni. - In: STOCHASTICS AND DYNAMICS. - ISSN 0219-4937. - STAMPA. - 8:(2008), pp. 413-449. [10.1142/S0219493708002391]
Some remarks concerning reflectionless Sturm-Liouville potentials
JOHNSON, RUSSELL ALLAN;
2008
Abstract
We consider the class of reflectionless Sturm-Liouville potentials and the subclass consisting of "Sato-Segal-Wilson" potentials. We construct illustrative examples lying in these classes, in particular we adapt the constructions of Craig and Levitan to the Sturm-Liouville case. We also discuss an inverse problem of Kotani type in the context of Sato-Segal-Wilson potentials.
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