Geodesic
A Sufficient Nonsingularity Condition for a Discrete Finite-Gap One-Energy Two-Dimensional Schr\"odinger Operator on the Quad-Graph
Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 3, pp. 65-70

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The finite-gap approach is used to construct a two-dimensional discrete Schrödinger operator on a quad-graph, that is, a planar graph whose faces are quadrangles. The following definition of the nonsingularity of this operator is proposed: An operator is nonsingular if all of its coefficients are positive. Conditions on a spectral curve and a quad-graph sufficient for the operator constructed from them to be nonsingular are given.
Keywords: discrete operator, discrete complex analysis, finite-gap operator, spectral curve, M-curve, Riemann surface, nonsingularity. 
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     author = {B. O. Vasilevskii},
     title = {A {Sufficient} {Nonsingularity} {Condition} for a {Discrete} {Finite-Gap} {One-Energy} {Two-Dimensional} {Schr\"odinger} {Operator} on the {Quad-Graph}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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     publisher = {mathdoc},
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B. O. Vasilevskii. A Sufficient Nonsingularity Condition for a Discrete Finite-Gap One-Energy Two-Dimensional Schr\"odinger Operator on the Quad-Graph. Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 3, pp. 65-70. http://geodesic.mathdoc.fr/item/FAA_2015_49_3_a5/