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Funktsional. Anal. i Prilozhen., 2015, Volume 49, Issue 3, Pages 65–70 (Mi faa3199)  

Brief communications

A Sufficient Nonsingularity Condition for a Discrete Finite-Gap One-Energy Two-Dimensional Schrödinger Operator on the Quad-Graph

B. O. Vasilevskii

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 2010-220-01-077


DOI: https://doi.org/10.4213/faa3199

Full text: PDF file (186 kB)
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English version:
Functional Analysis and Its Applications, 2015, 49:3, 210–213

Bibliographic databases:

UDC: 514.84
Received: 11.11.2013

Citation: B. O. Vasilevskii, “A Sufficient Nonsingularity Condition for a Discrete Finite-Gap One-Energy Two-Dimensional Schrödinger Operator on the Quad-Graph”, Funktsional. Anal. i Prilozhen., 49:3 (2015), 65–70; Funct. Anal. Appl., 49:3 (2015), 210–213

Citation in format AMSBIB
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