Geodesic
Estimates of the elements of inverse matrices for operators with banded matrices
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 3 (2000) no. 4, pp. 323-331

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In this paper, we have received the concrete estimates of the elements of inverse matrices for the bounded operators with banded (finite-diagonal) matrices acting in abstract Banach space. The method is based on the analysis of the Fourier series of some strongly continuous periodic operator-valued functions. 
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T. V. Azarnova; I. A. Kolesnikov. Estimates of the elements of inverse matrices for operators with banded matrices. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 3 (2000) no. 4, pp. 323-331. http://geodesic.mathdoc.fr/item/SJVM_2000_3_4_a3/