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Mat. Sb., 2002, Volume 193, Number 4, Pages 87–112 (Mi msb645)  

This article is cited in 1 scientific paper (total in 1 paper)

Spectral properties of two classes of periodic difference operators

A. A. Oblomkovab

a M. V. Lomonosov Moscow State University
b Independent University of Moscow

Abstract: A study is made of the iso-energetic spectral problem for two classes of multidimensional periodic difference operators. The first class of operators is defined on a regular simplicial lattice. The second class is defined on a standard rectangular lattice and is the difference analogue of a multidimensional Schrödinger operator. The varieties arising in the direct spectral problem are described, along with the divisor of an eigenfunction, defined on the spectral variety, of the corresponding operator. Multidimensional analogues are given for the Veselov–Novikov correspondences connecting the divisors of the eigenfunction with the canonical divisor of the spectral variety. Also, a method is proposed for solving the inverse spectral problem in terms of $\theta$-functions of curves lying “at infinity” on the spectral variety.

DOI: https://doi.org/10.4213/sm645

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English version:
Sbornik: Mathematics, 2002, 193:4, 559–584

Bibliographic databases:

UDC: 517.958
MSC: Primary 47B39; Secondary 39A70, 47A40, 35P05, 35J10, 35R30
Received: 18.04.2001

Citation: A. A. Oblomkov, “Spectral properties of two classes of periodic difference operators”, Mat. Sb., 193:4 (2002), 87–112; Sb. Math., 193:4 (2002), 559–584

Citation in format AMSBIB
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\pages 559--584
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  • https://doi.org/10.4213/sm645
  • http://mi.mathnet.ru/eng/msb/v193/i4/p87

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Oblomkov, “Isoenergy Spectral Problem for Multidimensional Difference Operators”, Funct. Anal. Appl., 36:2 (2002), 120–133  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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