标题： 代数曲线上的二维离散算子和有理函数 显示英文标题

标题： Two-dimensional discrete operators and rational functions on algebraic curves

摘要： 本文研究了在一能级上具有有限带的二维薛定谔算子与二维离散算子之间的联系。我们为一类新的二维可积离散算子找到了谱数据。这些算子的本征函数在零能级参数化为代数谱曲线上的点。对于亏格为一的谱曲线，我们证明了有限带薛定谔算子可以通过离散算子的极限获得。 显示英文摘要

摘要： In this paper we study a connection between finite-gap on one energy level two-dimensional Schrodinger operators and two-dimensional discrete operators. We find spectral data for a new class of two-dimensional integrable discrete operators. These operators have eigenfunctions on zero level energy parameterized by points of algebraic spectral curves. In the case of genus one spectral curves we show that the finite-gap Schrodinger operators can be obtained as a limit of the discrete operators.