Commuting differential operators
Teoretičeskaâ i matematičeskaâ fizika, Tome 162 (2010) no. 3, pp. 334-344
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider a model problem, related to Bessel functions, in the theory of commutative rings of linear differential operators with one independent variable. We construct new series of such commutative rings and give simple examples of rings with three generators.
Keywords: Bessel function, commuting ring of differential operators.
@article{TMF_2010_162_3_a1,
     author = {A. B. Shabat and Z. S. El'kanova},
     title = {Commuting differential operators},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {334--344},
     year = {2010},
     volume = {162},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_162_3_a1/}
}
TY  - JOUR
AU  - A. B. Shabat
AU  - Z. S. El'kanova
TI  - Commuting differential operators
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2010
SP  - 334
EP  - 344
VL  - 162
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2010_162_3_a1/
LA  - ru
ID  - TMF_2010_162_3_a1
ER  - 
%0 Journal Article
%A A. B. Shabat
%A Z. S. El'kanova
%T Commuting differential operators
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2010
%P 334-344
%V 162
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2010_162_3_a1/
%G ru
%F TMF_2010_162_3_a1
A. B. Shabat; Z. S. El'kanova. Commuting differential operators. Teoretičeskaâ i matematičeskaâ fizika, Tome 162 (2010) no. 3, pp. 334-344. http://geodesic.mathdoc.fr/item/TMF_2010_162_3_a1/

[1] E. T. Uitteker, Dzh. N. Vatson, Kurs sovremennogo analiza, Ch. 2, Fizmatlit, M., 1963 | MR | Zbl

[2] J. L. Burchnall, T. W. Chaundy, Proc. London Soc. Ser. 2, 21:1 (1923), 420–440 | DOI | MR | Zbl

[3] V. E. Adler, V. G. Marikhin, A. B. Shabat, TMF, 129:2 (2001), 163–183 | DOI | MR | Zbl

[4] J. A. Sanders, J. P. Wang, J. Differ. Equations, 147:2 (1998), 410–434 | DOI | MR | Zbl