Geodesic
Asymptotics of solutions of one-dimensional difference equations with constant operator coefficients
Sbornik. Mathematics, Tome 60 (1988) no. 2, pp. 437-455 
V. G. Maz'ya; M. G. Sulimov. Asymptotics of solutions of one-dimensional difference equations with constant operator coefficients. Sbornik. Mathematics, Tome 60 (1988) no. 2, pp. 437-455. http://geodesic.mathdoc.fr/item/SM_1988_60_2_a12/
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     author = {V. G. Maz'ya and M. G. Sulimov},
     title = {Asymptotics of solutions of one-dimensional difference equations with constant operator coefficients},
     journal = {Sbornik. Mathematics},
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     year = {1988},
     volume = {60},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_60_2_a12/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The authors study equations of the form $$ \sum_{k\geqslant0}A_ku_{n-k}=f_n,\qquad n=0,\pm1,\dots, $$ where the $u_n$ and $f_n$ are elements in some Hilbert space $H$, and the $A_k$ are bounded linear operators on $H$. It is assumed that the corresponding operator symbol $$ L(\lambda )=\sum_{k\geqslant0}A_k\lambda^k $$ is a holomorphic Fredholm operator-valued function which is normal in some neighborhood of zero. Bibliography: 9 titles.

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[2] Agmon S., Nirenberg L., “Properties of solutions of ordinary differential equations in Banach space”, Comm. Pure Appl. Math., 16 (1963), 121–239 | DOI | MR | Zbl

[3] Kondratev V. A., “Kraevye zadachi dlya ellipticheskikh uravnenii v oblastyakh s konicheskimi ili uglovymi tochkami”, Tr. MMO, 16 (1967), 209–292

[4] Mazya V. G., Plamenevskii B. A., “O koeffitsientakh v asimptotike reshenii ellipticheskikh kraevykh zadach v konuse”, Zap. nauchn. seminarov LOMI, 52 (1975), 110–127

[5] Faddeev D. K., Faddeeva V. N., Vychislitelnye metody lineinoi algebry, Fizmatgiz, M., 1960 | MR

[6] Markus A. S., “O golomorfnykh operator-funktsiyakh”, DAN SSSR, 119:6 (1958), 1099–1102 | MR | Zbl

[7] Trofimov V. P., “O kornevykh podprostranstvakh operatorov, analiticheski zavisyaschikh ot parametra”, Matem. issledovaniya, 3:3 (1968), 117–125 | MR | Zbl

[8] Markus A. S, Sigal E. I., “O kratnosti kharakteristicheskogo chisla analiticheskoi operator-funktsii”, Matem. issledovaniya, 5:3 (1970), 129–147 | MR | Zbl

[9] Riordan Dzh., Kombinatornye tozhdestva, Nauka, M., 1982 | MR | Zbl