ONE-DIMENSIONAL FINITE-GAP SCHRÖDINGER OPERATORS AS A LIMIT OF COMMUTING DIFFERENCE OPERATORS

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Abstract

In this paper we show that the one–dimensional finite–gap Schrödinger operator can be obtained by passing to the limit from a second–order difference operator that commutes with some odd–order difference operator; the coefficients of these difference operators are functions defined on the line and depend on a small parameter. Moreover, the spectral curve of the difference operators does not depend on the small parameter and coincides with the spectral curve of the Schrödinger operator.

About the authors

G. S. Mauleshova

Novosibirsk State University; Sobolev Institute of Mathematics

Author for correspondence.
Email: mauleshova@math.nsc.ru
Russian Federation, Novosibirsk; Russian Federation, Novosibirsk

A. E. Mironov

Novosibirsk State University; Sobolev Institute of Mathematics

Author for correspondence.
Email: mironov@math.nsc.ru
Russian Federation, Novosibirsk; Russian Federation, Novosibirsk

References

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