Geodesic
Isoenergy Spectral Problem for Multidimensional Difference Operators
Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 2, pp. 45-61

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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. 
@article{FAA_2002_36_2_a4,
     author = {A. A. Oblomkov},
     title = {Isoenergy {Spectral} {Problem} for {Multidimensional} {Difference} {Operators}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {45--61},
     publisher = {mathdoc},
     volume = {36},
     number = {2},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2002_36_2_a4/}
}
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A. A. Oblomkov. Isoenergy Spectral Problem for Multidimensional Difference Operators. Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 2, pp. 45-61. http://geodesic.mathdoc.fr/item/FAA_2002_36_2_a4/