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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2015, Volume 98, Issue 1, Pages 27–43 (Mi mz10450)

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

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).

DOI: https://doi.org/10.4213/mzm10450

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English version:
Mathematical Notes, 2015, 98:1, 38–52

Bibliographic databases:

UDC: 514.84
Revised: 30.10.2014

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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