Abstract
Let {Tn(t)}∞n=1 be a sequence of strongly continuous linear semigroups on Banach spaces Xn converging in the sense of Kato to a semigroup T(t) on the Banach space X. We discuss under what conditions the chaoticity of Tn(t) is inherited by T(t). We apply our results to a discrete parabolic equation.
| Original language | English |
|---|---|
| Pages (from-to) | 176-187 |
| Number of pages | 12 |
| Journal | Journal of Approximation Theory |
| Volume | 105 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jul 2000 |
Funding
We are extremely indebted to the referees who read the paper with unusual attention and care for detail. They made numerous valuable suggestions to improve the general style and the occasional casualness of the first version of the manuscript. V. P. was supported in part by the U.S. Department of Energy, Office of Basic Energy Sciences, under Contract DE-AC05-96OR22464 with Lockheed Martin Energy Research Corporation.
Keywords
- Hypercyclic and chaotic semigroups; approximation in the sense of Kato; convection-diffusion equation