Geodesic
The Green Function of the Discrete Finite-Gap One-Energy Two-Dimensional Schr\"odinger Operator on the Quad Graph
Matematičeskie zametki, Tome 98 (2015) no. 1, pp. 27-43

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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, Riemann sphere, Riemann surface, Iacobi manifold, quasimomentum.
Mots-clés : Cauchy–Riemann equations 
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     author = {B. O. Vasilevskii},
     title = {The {Green} {Function} of the {Discrete} {Finite-Gap} {One-Energy} {Two-Dimensional} {Schr\"odinger} {Operator} on the {Quad} {Graph}},
     journal = {Matemati\v{c}eskie zametki},
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B. O. Vasilevskii. The Green Function of the Discrete Finite-Gap One-Energy Two-Dimensional Schr\"odinger Operator on the Quad Graph. Matematičeskie zametki, Tome 98 (2015) no. 1, pp. 27-43. http://geodesic.mathdoc.fr/item/MZM_2015_98_1_a2/