Geodesic
Discrete analogues of Dixmier operators
Sbornik. Mathematics, Tome 198 (2007) no. 10, pp. 1433-1442 
A. E. Mironov. Discrete analogues of Dixmier operators. Sbornik. Mathematics, Tome 198 (2007) no. 10, pp. 1433-1442. http://geodesic.mathdoc.fr/item/SM_2007_198_10_a2/
@article{SM_2007_198_10_a2,
     author = {A. E. Mironov},
     title = {Discrete analogues of {Dixmier} operators},
     journal = {Sbornik. Mathematics},
     pages = {1433--1442},
     year = {2007},
     volume = {198},
     number = {10},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2007_198_10_a2/}
}
TY  - JOUR
AU  - A. E. Mironov
TI  - Discrete analogues of Dixmier operators
JO  - Sbornik. Mathematics
PY  - 2007
SP  - 1433
EP  - 1442
VL  - 198
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/SM_2007_198_10_a2/
LA  - en
ID  - SM_2007_198_10_a2
ER  - 
%0 Journal Article
%A A. E. Mironov
%T Discrete analogues of Dixmier operators
%J Sbornik. Mathematics
%D 2007
%P 1433-1442
%V 198
%N 10
%U http://geodesic.mathdoc.fr/item/SM_2007_198_10_a2/
%G en
%F SM_2007_198_10_a2

Voir la notice de l'article provenant de la source Math-Net.Ru

Discrete analogues of the Dixmier operators are found, which are commuting difference operators corresponding to a spectral curve of genus 1 with coefficients polynomial in the discrete variable $n$. Bibliography: 11 titles.

[1] J. L. Burchnall, T. W. Chaundy, “Commutative ordinary differential operators”, Proc. London Math. Soc., 21:1 (1923), 420–440 | DOI | Zbl

[2] I. M. Krichever, “Commutative rings of ordinary linear differential operators”, Funct. Anal. Appl., 12:3 (1978), 175–185 | DOI | MR | Zbl

[3] J. Dixmier, “Sur les algèbres de Weyl”, Bull. Soc. Math. France, 96 (1968), 209–242 | MR | Zbl

[4] I. M. Krichever, S. P. Novikov, “Holomorphic bundles over Riemann surfaces and the Kadomtsev–Petviashvili equation. I”, Funct. Anal. Appl., 12:4 (1978), 276–286 | DOI | MR | Zbl | Zbl

[5] P. G. Grinevich, “Rational solutions for the equation of commutation of differential operators”, Funct. Anal. Appl., 16:1 (1982), 15–19 | DOI | MR | Zbl

[6] O. I. Mokhov, “Commuting differential operators of rank 3, and nonlinear differential equations”, Math. USSR-Izv., 35:3 (1990), 629–655 | DOI | MR | Zbl

[7] A. E. Mironov, “A ring of commuting differential operators of rank 2 corresponding to a curve of genus 2”, Sb. Math., 195:5 (2004), 711–722 | DOI | MR | Zbl

[8] A. E. Mironov, “Commuting rank 2 differential operators corresponding to a curve of genus 2”, Funct. Anal. Appl., 39:3 (2005), 240–243 | DOI | MR | Zbl

[9] I. M. Krichever, S. P. Novikov, “Two-dimensionalized Toda lattice, commuting difference operators, and holomorphic bundles”, Russian Math. Surveys, 58:3 (2003), 473–510 | DOI | MR | Zbl

[10] D. Mumford, “An algebro-geometric construction of commuting operators and of solutions to the Toda lattice equation, Korteweg de Vries equation and related non-linear equations”, Proceedings of the International Symposium on Algebraic Geometry (Kyoto Univ., Kyoto, 1977), Kinokuniya, Tokyo, 1978, 115–153 | MR | Zbl

[11] I. M. Krichever, “Algebraic curves and non-linear difference equations”, Russian Math. Surveys, 33:4 (1978), 255–256 | DOI | MR | Zbl | Zbl