Isospectral Mathieu-Hill Operators

Author： Veliev O.  

Publisher： Springer Publishing Company

ISSN： 0377-9017

Source： Letters in Mathematical Physics, Vol.103, Iss.8, 2013-08, pp. : 919-925

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Abstract

In this paper we prove that the spectra of the Mathieu-Hill Operators with potentials ae−i2π x +be i2π x and ce−i2π x +de i2π x , where a, b, c and d are complex numbers, are the same if and only if ab = cd. This immediately results in a generalization of the extension of the Harrell-Avron-Simon formula.

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