On the mean ergodicity of weak solutions of an abstract evolution equation

Abstract

Found are conditions of rather general nature sufficient for the existence of the limit at infinity of the Cesàro means \begin{equation*} \frac{1}{t} \int_0^ty(s)\,ds \end{equation*} for every bounded weak solution $y(\cdot )$ of the abstract evolution equation \begin{equation*} y'(t)=Ay(t),\ t\ge 0, \end{equation*} with a closed linear operator $A$ in a Banach space $X$.

arXiv commentCorrected proof for the case of a scalar type spectral operator, added sources to bibliography, a number of readability improvements relative to the prior versions

References in corpus (1)

• On certain spectral features inherent to scalar type spectral operators

Cited by in corpus (1)

• On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator on the real axis