Isoenergy Spectral Problem for Multidimensional Difference Operators

A. A. Oblomkov<sup>ab

a</sup> Independent University of Moscow
^b M. V. Lomonosov Moscow State University

Abstract: In this paper, the direct and inverse isoenergy spectral problems are solved for a class of multidimensional periodic difference operators. It is proved that the inverse spectral problem is solvable in terms of theta functions of curves added to the spectral variety under compactification, and multidimensional analogs of the Veselov–Novikov relations are found.

Keywords: multidimensional scattering problem, Bloch function, spectral data.

UDC: 517.958

Received: 27.11.2000

DOI: 10.4213/faa190

 English version: Functional Analysis and Its Applications, 2002, 36:2, 120–133

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