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/

[1] Blatov I. A., “Ob otsenkakh elementov obratnykh matrits i o modifikatsiyakh metoda matrichnoi progonki”, Sib. matem. zhurn., 32:2 (1992), 10–21 | MR

[2] Baskakov A. G., Garmonicheskii analiz lineinykh operatorov, VGU, Voronezh, 1987 | MR

[3] Baskakov A. G., “Asimptoticheskie otsenki elementov matrits obratnykh operatorov i garmonicheskii analiz”, Sib. matem. zhurn., 38:1 (1997), 14–28 | MR | Zbl

[4] Baskakov A. G., “Abstraktnyi garmonicheskii analiz i asimptoticheskie otsenki elementov obratnykh matrits”, Mat. zam., 52:2 (1992), 17–25 | MR

[5] Shubin M. A., “Psevdoraznostnye operatory i ikh funktsiya Grina”, Izvestiya AN SSSR, ser. matem., 49:3 (1985), 652–671 | MR | Zbl

[6] Demko S., Moss F., Smith W., “Decay rates for inverses of band matrices”, Math. Comput., 43 (1984), 491–499 | MR | Zbl

[7] Azarnova T. V., “Otsenki elementov obratnykh matrits dlya nekotorykh klassov lineinykh ogranichennykh operatorov”, Izvestiya VUZov, matematika, 1998, no. 3(430), 74–77 | MR | Zbl

[8] Baskakov A. G., “Otsenki elementov obratnykh matrits i spektralnyi analiz lineinykh operatorov”, Izvestiya RAN, seriya matem., 61:6 (1997), 3–26 | MR | Zbl

[9] Danford N., Shvarts Dzh., Lineinye operatory. Obschaya teoriya, Inostr. lit., Moskva, 1962