Dynamics and spectrum of the Cesàro operator on \(C^\infty ({\mathbb R}_+)\)

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• 作者：Angela A. Albanese ; José Bonet ; Werner J. Ricker
• 关键词：Cesàro operator ; Fréchet space of smooth functions ; Spectrum ; Mean ergodic operator ; \(C_0\) ; semigroup
• 刊名：Monatshefte f¨¹r Mathematik
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：181
• 期：2
• 页码：267-283
• 全文大小：496 KB
• 刊物主题：Mathematics, general;
• 出版者：Springer Vienna
• ISSN：1436-5081
• 卷排序：181

文摘

The spectrum and point spectrum of the Cesàro averaging operator \(\mathsf {C}\) acting on the Fréchet space \(C^\infty ({\mathbb R}_+)\) of all \(C^\infty \) functions on the interval \([0,\infty )\) are determined. We employ an approach via \(C_0\)-semigroup theory for linear operators. A spectral mapping theorem for the resolvent of a closed operator acting on a locally convex space is established; it constitutes a useful tool needed to establish the main result. The dynamical behaviour of \(\mathsf {C}\) is also investigated.