One-Dimensional Finite-Gap Schrodinger Operators As a Limit of Commuting Difference Operators

In this paper we show that the one-dimensional finite-gap Schrodinger operator can be obtained via passage 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 Schrodinger operator.