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

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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. 
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     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},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {1971},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1971_5_3_a12/}
}
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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/