This article is cited in 9 scientific papers (total in 9 papers)
On spectral properties of operators with a shift
A. B. Antonevich, A. V. Lebedev
A formula is obtained for the spectral radius of a weighted shift operator for a broad class of spaces in the case of an arbitrary invertible shift, and some general theorems are proved about properties of the spectrum for such operators. Necessary and sufficient conditions are found for invertibility of two-term operators with a shift.
Bibliography: 39 titles.
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Mathematics of the USSR-Izvestiya, 1984, 23:2, 201–224
MSC: Primary 47A10, 47B37; Secondary 47A35, 57R50, 58F09, 58F11
A. B. Antonevich, A. V. Lebedev, “On spectral properties of operators with a shift”, Izv. Akad. Nauk SSSR Ser. Mat., 47:5 (1983), 915–941; Math. USSR-Izv., 23:2 (1984), 201–224
Citation in format AMSBIB
\by A.~B.~Antonevich, A.~V.~Lebedev
\paper On spectral properties of operators with a~shift
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
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Abramovich I., Arenson E., Kitover A., “Operators in Banach C(K)-Modules and their Spectral Properties”, 301, no. 3, 1988, 525–528
A. B. Antonevich, “Boundary value problems with strong nonlocalness for elliptic equations”, Math. USSR-Izv., 34:1 (1990), 1–21
Karlovich I., “On Algebras of Singular Integral-Operators with Discrete-Groups of Shifts in Lp Spaces”, 304, no. 2, 1989, 274–280
A. K. Kitover, “Rotation operators with multiplication and some of their generalizations”, Funct. Anal. Appl., 24:1 (1990), 70–72
Yu. D. Latushkin, A. M. Stepin, “Weighted translation operators and linear extensions of dynamical systems”, Russian Math. Surveys, 46:2 (1991), 95–165
Campbell J., Latushkin Y., “Sharp Estimates in Ruelle Theorems for Matrix Transfer Operators”, Commun. Math. Phys., 185:2 (1997), 379–396
Gundlach V., Latushkin Y., “A Sharp Formula for the Essential Spectral Radius of the Ruelle Transfer Operator on Smooth and Holder Spaces”, Ergod. Theory Dyn. Syst., 23:Part 1 (2003), 175–191
Antonevich A.B., Bakhtin V.I., Lebedev A.V., “On T-Entropy and Variational Principle for the Spectral Radii of Transfer and Weighted Shift Operators”, Ergod. Theory Dyn. Syst., 31:4 (2011), 995–1042
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