Geodesic
On Meromorphic Solutions of Two-Dimensional Difference Equations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 3, pp. 360-369.

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

We study the structure of meromorphic solutions to difference equations by means of integral representations.
Keywords: difference equations, special functions, hypergeometric functions. 
@article{JSFU_2009_2_3_a11,
     author = {Pavel V. Trishin},
     title = {On {Meromorphic} {Solutions} of {Two-Dimensional} {Difference} {Equations}},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {360--369},
     publisher = {mathdoc},
     volume = {2},
     number = {3},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2009_2_3_a11/}
}
TY  - JOUR
AU  - Pavel V. Trishin
TI  - On Meromorphic Solutions of Two-Dimensional Difference Equations
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2009
SP  - 360
EP  - 369
VL  - 2
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2009_2_3_a11/
LA  - ru
ID  - JSFU_2009_2_3_a11
ER  - 
%0 Journal Article
%A Pavel V. Trishin
%T On Meromorphic Solutions of Two-Dimensional Difference Equations
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2009
%P 360-369
%V 2
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2009_2_3_a11/
%G ru
%F JSFU_2009_2_3_a11
Pavel V. Trishin. On Meromorphic Solutions of Two-Dimensional Difference Equations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 3, pp. 360-369. http://geodesic.mathdoc.fr/item/JSFU_2009_2_3_a11/

[1] V. M. Trutnev, A. K. Tsikh, “O strukture vychetnykh potokov i funktsionalov, ortogonalnykh idealam v prostranstve golomorfnykh funktsii”, Izv. RAN. Ser. matem., 59:5 (1995), 203–224 | MR | Zbl

[2] E. K. Leinartas, “Kratnye ryady Lorana i raznostnye uravneniya”, Sib. mat. zhurn., 45:2 (2004), 387–393 | MR | Zbl

[3] B. V. Shabat, Vvedenie v kompleksnyi analiz, Ch. 2, Nauka, M., 1985 | MR

[4] A. A. Mirolyubov, M. A. Soldatov, Lineinye odnorodnye raznostnye uravneniya, Nauka, M., 1981 | MR | Zbl

[5] A. S. Krivosheev, V. V. Napalkov, “Kompleksnyi analiz i operatory svertki”, Uspekhi mat. nauk, 47:6 (1992), 3–58 | MR | Zbl

[6] V. M. Trutnev, “Prodolzhenie golomorfnykh reshenii raznostnykh uravnenii”, Mnogomernyi kompleksnyi analiz, Krasnoyar. gos. un-t, Krasnoyarsk, 2002, 172–177

[7] E. M. Chirka, Kompleksnye analiticheskie mnozhestva, Nauka, M., 1985 | MR | Zbl

[8] I. M. Gelfand, “Obschaya teoriya gipergeometricheskikh funktsii”, Dokl. AN SSSR, 290:1 (1986), 14–18

[9] V. A. Vasilev, Vetvyaschiesya integraly, MTsNMO, M., 2000

[10] Zh. Lere, Differentsialnoe i integralnoe ischislenie na kompleksnom analiticheskom mnogoobrazii, Inostr. lit., M., 1961 | MR

[11] L. A. Aizenberg, A. P. Yuzhakov, Integralnye predstavleniya i vychety v mnogomernom kompleksnom analize, Nauka, Novosibirsk, 1979 | MR

[12] M. Forsberg, M. Passare, A. Tsikh, “Laurent determinants and arrangements of hyperplane amoebas”, Adv. in Math., 151 (2000), 54–70 | DOI | MR

[13] M. F. Atiyah, “Resolution of singularities and division of distributions”, Comm. Pure Appl. Math., 23:2 (1970), 145–150 | DOI | MR | Zbl