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C0‐continuity of the Fröbenius‐Perron semigroup

International Journal of Mathematics and Mathematical Sciences, Volume 31, Issue 5, Page 307-319, 2002., 2002
We consider the Fröbenius‐Perron semigroup of linear operators associated to a semidynamical system defined in a topological space X endowed with a finite or a σ‐finite regular measure. We prove that if there exists a faithful invariant measure for the semidynamical system, then the Fröbenius‐Perron semigroup of linear operators is C0‐continuous in the
Andrés Navas, Sergio Plaza
wiley   +1 more source

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

Open Mathematics, 2020
Given the abstract evolution equation y′(t)=Ay(t),t∈ℝ,y^{\prime} (t)=Ay(t),t\in {\mathbb{R}}, with a scalar type spectral operator A in a complex Banach space, we find conditions on A, formulated exclusively in terms of the location of its spectrum in ...
Markin Marat V.
doaj   +1 more source

On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator of orders less than one

Open Mathematics, 2019
It is shown that, if all weak solutions of the evolution ...
Markin Marat V.
doaj   +1 more source

Solving Becker’s Problem on Periodic Solutions of Parabolic Evolution Equations

Advanced Nonlinear Studies, 2018
We present existence and multiplicity theorems for periodic mild solutions to parabolic evolution equations. Their peculiarity is a link with the spectrum of the generator of the semigroup rather than with the spectrum of the linearized periodic BVP for ...
Vidossich Giovanni
doaj   +1 more source

On the Gevrey ultradifferentiability of weak solutions of an abstract evolution equation with a scalar type spectral operator on the open semi-axis

Open Mathematics, 2019
Given the abstract evolution ...
Markin Marat V.
doaj   +1 more source