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Matematicheskie Zametki, 2015, Volume 98, Issue 1, Pages 27–43
DOI: https://doi.org/10.4213/mzm10450 (Mi mzm10450) 		 
The Green Function of the Discrete Finite-Gap One-Energy Two-Dimensional Schrödinger Operator on the Quad Graph

B. O. Vasilevskii

Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm10450
Abstract: The finite-gap approach to constructing the discrete Schrödinger operator on a quad graph expressed as a two-dimensional integer sublattice in $d$-dimensional space is used. The Green function for this operator is explicitly expressed as an integral over special contours of the differential constructed from spectral data. The resulting function has a well-known asymptotics.
Keywords: discrete Schrödinger operator, Green function, integer sublattice, quad graph, wave function, Cauchy–Riemann equations, Riemann sphere, Riemann surface, Iacobi manifold, quasimomentum.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 2010-220-01-077
This work was supported by the Government of the Russian Federation (grant no. 2010-220-01-077).
Received: 07.01.2014
Revised: 30.10.2014
English version:
Mathematical Notes, 2015, Volume 98, Issue 1, Pages 38–52
DOI: https://doi.org/10.1134/S0001434615070044
Bibliographic databases:
Document Type: Article
UDC: 514.84
Language: Russian
Citation: B. O. Vasilevskii, “The Green Function of the Discrete Finite-Gap One-Energy Two-Dimensional Schrödinger Operator on the Quad Graph”, Mat. Zametki, 98:1 (2015), 27–43; Math. Notes, 98:1 (2015), 38–52
Citation in format AMSBIB
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