Abstract
In fact, Hochstadt gives an explicit formula for the discriminant which will be reproduced below. Since Hochstadt’s work there has been a considerable interest in finite-band potentials, i.e., potentials q such that the spectrum of the operator associated with d2/dx 2 + q consists of finitely many regular analytic arcs, due to their close relationship with the Korteweg-de Vries hierarchy and hence with integrable systems. However, the interest is not restricted to real-valued potentials. For instance,
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