Geodesic
Harmonic and Spectral Analysis of Power Bounded Operators and Bounded Semigroups of Operators on Banach Spaces
Matematičeskie zametki, Tome 97 (2015) no. 2, pp. 174-190

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Asymptotic representations of power bounded operators and bounded semigroups of linear operators acting in Banach spaces are obtained under the assumptions that the spectrum of bounded operators on the unit circle and the spectrum of the semigroup generator on the imaginary axis are countable. The methods of abstract harmonic analysis and the spectral theory of operators were used.
Keywords: power bounded operator, operator semigroup, harmonic analysis, spectral theory, asymptotic representation, Banach algebra. 
@article{MZM_2015_97_2_a1,
     author = {A. G. Baskakov},
     title = {Harmonic and {Spectral} {Analysis} of {Power} {Bounded} {Operators} and {Bounded} {Semigroups} of {Operators} on {Banach} {Spaces}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {174--190},
     publisher = {mathdoc},
     volume = {97},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_97_2_a1/}
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A. G. Baskakov. Harmonic and Spectral Analysis of Power Bounded Operators and Bounded Semigroups of Operators on Banach Spaces. Matematičeskie zametki, Tome 97 (2015) no. 2, pp. 174-190. http://geodesic.mathdoc.fr/item/MZM_2015_97_2_a1/