Abstract
As an application of the results on the dynamics of a linear map some results on spectral properties of weighted shift operators are presented below.
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References
Antonevich, A. B. (1988). Linear functional equations. Operator approach (English transl. Birkhauser, Basel, Boston, Berlin, 1996). Minsk: Universitetskoe (in Russian).
Chicone, C., & Latushkin, Yu. (1999). Evolution semigroups in dynamical systems and differential equations. Providence: AMS.
Antonevich, A., & Lebedev, A. (1994). Functional differential equations: I. \(C^*\) -theory. Harlow: Longman Scientific & Technical.
Antonevich, A., & Lebedev A. (1998). Functional and functional-differential equations. \( A C^*-\) algebraic approach (English transl. in Amer. Math. Soc. Transl. Ser. 2. 1999, pp. 25–116). Trudy Sankt-Peterburgskogo Matematicheskogo Obshchestva, 6, 34–140.
Gelfond, A. O. (1967). Finite differences calculus. Moscow: Nauka.
Hale, J. (1977). Theory of functional differential equations. New York-Heidelberg-Berlin: Springer.
Halmos, P. (1956). Ergodic theory. New York: Chelsea.
Karapetiants, N., & Samko, S. (2001). Equations with involutive operators. Birkh\(\ddot{a}\)user: Boston-Basel-Berlin.
Kravchenko, V. G., & Litvinchuk, G. S. (1994). Introduction to the theory of singular integral operators with shift, mathematics and its applications (Vol. 289). Dordrecht: Kluwer.
Kolmanovsli, V. B., & Nosov, V. R. (1981). Stability and periodic condition of controlled systems with aftereffects. Moscow: Nauka.
Kornfeld, I. P., Sinai, Y. G., & Fomin, S. V. (1980). Ergodic theory. Moscow: Nauka.
Katok, A., & Hasselblatt, B. (1998). Introduction to the modern theory of dynamical systems. Cambridge: Cambridge University Press.
Skubachevskii, A. L. (1997). Elliptic functional differential equations and applications. Birkh\(\ddot{\text{ a }}\)user: Basel-Boston-Berlin.
Antonevich, A. B. (1975). On a class of pseudodifferential opearators with deviating argument on the torus. Differentsial’nye Uravneniya, 11(9), 1550–1557.
Antonevich, A. B. (1979). Operators with a shift generated by the action of a compact Lie group. Sibirskii Matematicheskii Zhurnal, 20(3), 467–478.
Daniluk, A., & Stochel, J. (1997). Seminormal composition operators induced by affine transformations. Hokkaido Mathematical Journal, XXVI(2), 377–404.
Stochel, J. (1990). Seminormal composition operators on \(L^2\) spaces induced by matrices. Hokkaido Mathematical Journal, 19, 307–324.
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Dolićanin, Ć.B., Antonevich, A.B. (2014). The Spectrum of Weighted Shift Operator. In: Dynamical Systems Generated by Linear Maps. Springer, Cham. https://doi.org/10.1007/978-3-319-08228-8_13
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DOI: https://doi.org/10.1007/978-3-319-08228-8_13
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