Geodesic
Necessary and sufficient criteria for the boundedness of the solutions of certain systems of linear difference equations in Banach space
Izvestiya. Mathematics, Tome 5 (1971) no. 3, pp. 719-729 
I. I. Marmershtein. Necessary and sufficient criteria for the boundedness of the solutions of certain systems of linear difference equations in Banach space. Izvestiya. Mathematics, Tome 5 (1971) no. 3, pp. 719-729. http://geodesic.mathdoc.fr/item/IM2_1971_5_3_a12/
@article{IM2_1971_5_3_a12,
     author = {I. I. Marmershtein},
     title = {Necessary and sufficient criteria for the boundedness of the solutions of certain systems of linear difference equations in {Banach} space},
     journal = {Izvestiya. Mathematics},
     pages = {719--729},
     year = {1971},
     volume = {5},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1971_5_3_a12/}
}
TY  - JOUR
AU  - I. I. Marmershtein
TI  - Necessary and sufficient criteria for the boundedness of the solutions of certain systems of linear difference equations in Banach space
JO  - Izvestiya. Mathematics
PY  - 1971
SP  - 719
EP  - 729
VL  - 5
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/IM2_1971_5_3_a12/
LA  - en
ID  - IM2_1971_5_3_a12
ER  - 
%0 Journal Article
%A I. I. Marmershtein
%T Necessary and sufficient criteria for the boundedness of the solutions of certain systems of linear difference equations in Banach space
%J Izvestiya. Mathematics
%D 1971
%P 719-729
%V 5
%N 3
%U http://geodesic.mathdoc.fr/item/IM2_1971_5_3_a12/
%G en
%F IM2_1971_5_3_a12

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

In the present article exact (necessary and sufficient) spectral criteria are found for the stability of the solutions of certain systems of linear partial difference equations in Banach space.

[1] Marmershtein I. I., “Ob ogranichennosti reshenii nekotorykh sistem lineinykh uravnenii v chastnykh raznostyakh”, Dokl. AN SSSR, 189:3 (1969), 475–478

[2] Marmershtein I. I., “Ob ustoichivosti reshenii odnogo klassa lineinykh raznostnykh uravnenii”, Izv. vuzov. Matematika, 1968, no. 7, 37–41 | Zbl

[3] Rutman M. A., Avtoreferat doktorskoi dissertatsii, LGU, 1960

[4] Rutman M. A., “Ob ogranichennosti reshenii nekotorykh lineinykh uravnenii v chastnykh raznostyakh”, Dokl. AN SSSR, 159:2 (1964), 273–275 | MR | Zbl

[5] Rutman M. A., “Kriterii ogranichennosti reshenii dlya lineinykh differentsialnykh uravnenii s chastnymi proizvodnymi, obladayuschikh starshim chlenom”, Dokl. AN SSSR, 147:4 (1962), 789–792 | MR | Zbl

[6] Rutman M. A., “Ob ustoichivosti reshenii nekotorykh sistem lineinykh differentsialnykh uravnenii s peremennymi koeffitsientami”, Dokl. AN SSSR, 108:5 (1956), 770–773 | MR | Zbl

[7] Melamed E. Ya., “Ob ustoichivosti reshenii nekotorykh differentsialnykh kraevykh zadach s chastnymi proizvodnymi v banakhovom prostranstve”, Dokl. AN SSSR, 120:6 (1958), 1194–1195 | MR | Zbl