# Perturbations of bi-continuous semigroups

@article{Farkas2004PerturbationsOB, title={Perturbations of bi-continuous semigroups}, author={B{\'a}lint Farkas}, journal={Studia Mathematica}, year={2004}, volume={161}, pages={147-161} }

initial value problems (Cauchy problems) are usually studied via operator semigroups. In many cases, the well-developed theory of C0-semigroups, i.e., one-parameter operator semigroups which are strongly continuous for the norm on a Banach space X , suffices and provides a powerful machinery to study such problems. The applications range from partial differential equations, Volterra integro-differential equations and dynamic boundary problems to delay equations. It seems that a linear…

## 31 Citations

General Extrapolation Spaces and Perturbations of Bi-Continuous Semigroups

- Mathematics
- 2019

A lot of well-known partial differential equations modeling physical systems, such as the heat
equation, the Schrodinger equation or the wave equation, use temporal change of states. Evolution …

On continuity properties of semigroups in real interpolation spaces

- Journal of Evolution Equations
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Starting from a bi-continuous semigroup in a Banach space X (which might actually be strongly continuous), we investigate continuity properties of the semigroup that is induced in real interpolation…

Evolution Semigroups for Well-Posed, Non-Autonomous Evolution Families

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- 2016

The goal of this dissertation is to expand Berhard Koopman’s operator theoretic global linearization approach to the study of nonautonomous flows. Given a system with states x in a set Ω (the state…

Adjoint bi-continuous semigroups and semigroups on the space of measures

- Mathematics
- 2008

For a given bi-continuous semigroup (T(t))t⩾0 on a Banach space X we define its adjoint on an appropriate closed subspace X° of the norm dual X′. Under some abstract conditions this adjoint semigroup…

A Desch–Schappacher perturbation theorem for bi‐continuous semigroups

- Mathematics
- 2018

We prove a Desch-Schappacher type perturbation theorem for one-parameter semigroups on Banach spaces which are not strongly continuous for the norm, but possess a weaker continuity property. In this…

Uniform convergence to equilibrium for coupled parabolic PDEs and linear evolution equations

- Mathematics
- 2020

We consider systems of heat equations, subject to Neumann boundary conditions or on the whole space $\mathbb{R}^d$, that are coupled by a matrix-valued potential $V$. Our main question is under which…

Rational approximation schemes for bi-continuous semigroups

- Mathematics
- 2008

Abstract This paper extends the Hille–Phillips functional calculus and rational approximations results due to R. Hersh, T. Kato, P. Brenner, and V. Thomee to generators of bi-continuous semigroups.…

Euler’s Exponential Formula for Semigroups

- Mathematics
- 2004

Abstract
The aim of this paper is to show that Euler’s exponential formula
$\lim_{n\rightarrow\infty}\linebreak[4] (I-tA/n)^{-n}x = e^{tA}x$, well known for
$C_0$ semigroups in a Banach space $X\ni…

Perturbations of Bi-continuous Semigroups with
Applications to Transition Semigroups on Cb(H)

- Mathematics
- 2004

AbstractWe prove an unbounded perturbation theorem for bi-continuous semigroups on the space of bounded,
continuous functions on the Hilbert space H. This is applied to the Ornstein-Uhlenbeck…

Mean ergodic theorems for bi-continuous semigroups

- Mathematics
- 2009

In this paper we study the main properties of the Cesàro means of bi-continuous semigroups, introduced and studied by Kühnemund (Semigroup Forum 67:205–225, 2003). We also give some applications to…

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