Polynomial stability of evolution operators in Banach spaces
The paper considers three concepts of polynomial stability for linear evolution operators which are defined in a general Banach space and whose norms can increase not faster than exponentially. Our approach is based on the extension of techniques for exponential stability to the case of polynomial stability. Some illustrating examples clarify the relations between the stability concepts considered in paper. The obtained results are generalizations of well-known theorems about the uniform and nonuniform exponential stability.
On nonuniform exponential stability for skew-evolution semiflows on Banach spaces
The paper considers some concepts of nonuniform asymptotic stability for skew-evolution semiflows on Banach spaces. The obtained results clarify differences between the uniform and nonuniform cases. Some examples are included to illustrate the results.
Points of strong summability of Fourier series
In this paper we present a new solution of Hardy and Littlewood's problem concerning strong summability of Fourier series; we also present a property of points of strong summability.