On commuting differential operators of rank~$2$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 6 (2009), pp. 533-536.

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

In this work we suggest the method of constructing of commuting ordinary differential operators of rank $2$ corresponding to the spectral curve of genus $3$ and $4$. In the case of genus $4$ the operators have polynomial coefficients.
Keywords: commuting differential operators.
@article{SEMR_2009_6_a31,
     author = {A. E. Mironov},
     title = {On commuting differential operators of rank~$2$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {533--536},
     publisher = {mathdoc},
     volume = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2009_6_a31/}
}
TY  - JOUR
AU  - A. E. Mironov
TI  - On commuting differential operators of rank~$2$
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2009
SP  - 533
EP  - 536
VL  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2009_6_a31/
LA  - ru
ID  - SEMR_2009_6_a31
ER  - 
%0 Journal Article
%A A. E. Mironov
%T On commuting differential operators of rank~$2$
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2009
%P 533-536
%V 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2009_6_a31/
%G ru
%F SEMR_2009_6_a31
A. E. Mironov. On commuting differential operators of rank~$2$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 6 (2009), pp. 533-536. http://geodesic.mathdoc.fr/item/SEMR_2009_6_a31/

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

[2] I. M. Krichever, S. P. Novikov, “Golomorfnye rassloeniya nad rimanovymi poverkhnostyami i uravnenie Kadomtseva–Petviashvili. 1”, Funkts. analiz. i ego prilozh., 12:4 (1978), 41–52 | MR | Zbl

[3] I. M. Krichever, S. P. Novikov, “Golomorfnye rassloeniya nad algebraicheskimi krivymi i nelineinye uravneniya”, Uspekhi matem. nauk., 35:6 (1980), 47–68 | MR | Zbl

[4] P. G. Grinevich, “Ratsionalnye resheniya uravnenii kommutatsii differentsialnykh operatorov”, Funkts. analiz. i ego prilozh., 16:1 (1982), 19–24 | MR | Zbl

[5] O. I. Mokhov, “Kommutiruyuschie differentsialnye operatory ranga 3 i nelineinye uravneniya”, Izvestiya AN SSSR. Seriya matem., 53:6 (1989), 1291–1314

[6] A. E. Mironov, “Ob odnom koltse kommutiruyuschikh differentsialnykh operatorov ranga dva, otvechayuschem krivoi roda dva”, Matem. sb., 195:5 (2004), 103–114 | MR | Zbl

[7] A. E. Mironov, “Kommutiruyuschie differentsialnye operatory ranga 2, otvechayuschie krivoi roda 2”, Funkts. analiz i ego pril., 39:3 (2005), 91–94 | MR | Zbl

[8] I. M. Krichever, “Kommutativnye koltsa lineinykh obyknovennykh differentsialnykh operatorov”, Funkts. analiz. i ego prilozh., 12:3 (1978), 20–31 | MR | Zbl