Linear Chaos and Approximation

R. Delaubenfels; H. Emamirad; V. Protopopescu

doi:10.1006/jath.2000.3465

Linear Chaos and Approximation

R. Delaubenfels
, H. Emamirad
, V. Protopopescu

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

Let {T_n(t)}^∞_n=1 be a sequence of strongly continuous linear semigroups on Banach spaces X_n converging in the sense of Kato to a semigroup T(t) on the Banach space X. We discuss under what conditions the chaoticity of T_n(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	https://doi.org/10.1006/jath.2000.3465
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

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10.1006/jath.2000.3465

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AB - 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.

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Linear Chaos and Approximation

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