Estimates for the entries of inverse matrices and the spectral analysis of linear operators
Izvestiya. Mathematics, Tome 61 (1997) no. 6, pp. 1113-1135 Cet article a éte moissonné depuis la source Math-Net.Ru

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Using the representation theory of Abelian groups, we estimate the entries of inverse matrices of linear operators and apply the results to the spectral theory of linear operators.
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A. G. Baskakov. Estimates for the entries of inverse matrices and the spectral analysis of linear operators. Izvestiya. Mathematics, Tome 61 (1997) no. 6, pp. 1113-1135. http://geodesic.mathdoc.fr/item/IM2_1997_61_6_a0/

[1] De Boor C., “A bound on the $L_{\infty }$-norm of the $L_2$-approximation by splines in terms of a global mesh ratio”, Math. Comp., 30 (1976), 687–694 | DOI | MR

[2] Mityagin B., “Quadratic pencils and least-squares piecewise-polynomial approximation”, Math. Comp., 40 (1983), 283–300 | DOI | MR | Zbl

[3] Blatov I. A., Terteryan A. A., “Ob otsenkakh elementov obratnykh matrits i metodakh nepolnoi blochnoi faktorizatsii na osnove matrichnoi progonki”, ZhVMiMF, 32:11 (1992), 1683–1696 | MR | Zbl

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

[5] Kurbatov V. G., “Ob algebrakh raznostnykh i integralnykh operatorov”, Funkts. analiz i ego prilozh., 24:2 (1990), 87–88 | MR | Zbl

[6] Baskakov A. G., “Teorema Vinera i asimptoticheskie otsenki elementov obratnykh matrits”, Funkts. analiz i ego prilozh., 24:3 (1990), 64–65 | MR | Zbl

[7] Baskakov A. G., “Abstraktnyi garmonicheskii analiz i asimptoticheskie otsenki elementov obratnykh matrits”, Matem. zametki, 52:2 (1992), 17–26 | MR | Zbl

[8] Bochner S., Fillips R. S., “Absolute convergent Fourier expension for non-commutative normed rings”, Ann. of Math., 1942, no. 3, 409–418 | DOI | MR | Zbl

[9] Allan G. R., “Ideals of vector-valued functions”, Proc. London Math. Soc., 18:3 (1968), 193–216 | DOI | MR | Zbl

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

[11] Demko S., “Spectral Bounds for $\|A^{-1}\|_{\infty }$”, J. of Approxim. Theory, 48 (1986), 207–212 | DOI | MR | Zbl

[12] Demko S., Moss W. F., Smith P. W., “Decay Rates for Inverses of Band Matrices”, Math. Comp., 43:168 (1984), 491–499 | DOI | MR | Zbl

[13] De Boor C., “Dichotomies for band matrices”, SIAM. J. Numer. Anal., 17 (1980), 894–907 | DOI | MR | Zbl

[14] Baskakov A. G., “O spektralnykh svoistvakh nekotorykh klassov lineinykh operatorov”, Funkts. analiz i ego prilozh., 29:2 (1995), 61–64 | MR | Zbl

[15] Lyubich Yu. I., Matsaev V. I., “Ob operatorakh s otdelimym spektrom”, Matem. sb., 56:4 (1962), 433–468 | MR

[16] Baskakov A. G., “Metody abstraktnogo garmonicheskogo analiza v teorii vozmuschenii lineinykh operatorov”, Sib. matem. zhurn., 24:1 (1983), 21–39 | MR

[17] Baskakov A. G., Garmonicheskii analiz lineinykh operatorov, Izd-vo VGU, Voronezh, 1987 | MR | Zbl

[18] Baskakov A. G., “Garmonicheskii analiz kosinusnoi i eksponentsialnoi operatornoi funktsii”, Matem. sb., 124:5 (1984), 68–95 | MR | Zbl

[19] Colojoara I., Foias C., Theory of generalized spectral operators, Gordon and Breach, New York, 1968 | MR | Zbl

[20] Danford N., Shvarts Dzh. T., Lineinye operatory. Spektralnye operatory, T. III, Mir, M., 1974

[21] Dynkin E. M., “Teoremy tipa Vinera–Levi i otsenki dlya operatorov Vinera–Khopfa”, Matem. issl. (Kishinev), 8, no. 3(29), 1973, 14–25 | MR | Zbl