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arXiv · 1402.1938

A sufficient condition for nonsingularity of two-dimensional finite-gap Schr\"{o}dinger operator discretization of a quad graph

Vasilevskiy Boris
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Abstract

We construct a two-dimensional Schr\"{o}dinger operator on a quad-graph using finite-gap approach. A guad-graph is a planar graph with only 4-sided faces. We define the non-singularity of the operator as the positivity of all of his coefficients. At last, we prove some sufficient conditions of such positivity on the spectral curve and the graph.

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Vasilevskiy Boris. 2014-02-09. A sufficient condition for nonsingularity of two-dimensional finite-gap Schr\"{o}dinger operator discretization of a quad graph. https://arxiv.org/abs/1402.1938

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