Harmonic and Spectral Analysis of Power Bounded Operators and Bounded Semigroups of Operators on Banach Spaces

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.