Geodesic
Asymptotics of solutions of one-dimensional difference equations with constant operator coefficients
Sbornik. Mathematics, Tome 60 (1988) no. 2, pp. 437-455

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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. 
@article{SM_1988_60_2_a12,
     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},
     pages = {437--455},
     publisher = {mathdoc},
     volume = {60},
     number = {2},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_60_2_a12/}
}
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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/