Dynamics and spectrum of the Cesàro operator on \(C^\infty (\mathbb R_+)\)

DOI10.1007/s00605-015-0863-zzbMath1358.47003OpenAlexW2231758183MaRDI QIDQ328579

Angela A. Albanese, José Bonet, Werner J. Ricker

Publication date: 20 October 2016

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00605-015-0863-z

zbMATH Keywords

spectrum\(C_0\)-semigroupCesàro operatormean ergodic operatorFréchet space of smooth functions

Mathematics Subject Classification ID

One-parameter semigroups and linear evolution equations (47D06) Ergodic theory of linear operators (47A35) Spectrum, resolvent (47A10) Linear operators on function spaces (general) (47B38) Topological linear spaces of continuous, differentiable or analytic functions (46E10) Locally convex Fréchet spaces and (DF)-spaces (46A04) Cyclic vectors, hypercyclic and chaotic operators (47A16)

Related Items (4)

On the spectrum of isomorphisms defined on the space of smooth functions which are flat at $0$ ⋮ Spectrum of the Cesàro operator on the ultradifferentiable function spaces \(\mathcal{E}_\omega (\mathbb{R}_+)\) ⋮ Spectrum of composition operators on \(\mathcal{S}(\mathbb{R})\) with polynomial symbols ⋮ Surjectivity of Euler type differential operators on spaces of smooth functions

Cites Work

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• On the continuous Cesàro operator in certain function spaces
• Linear chaos
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• Gaussian estimates and interpolation of the spectrum in \(L^ p\)
• Mean ergodic semigroups of operators
• Convergence of arithmetic means of operators in Fréchet spaces
• Semigroups of operators in locally convex spaces
• Montel resolvents and uniformly mean ergodic semigroups of linear operators
• THE CESÀRO OPERATOR IN THE FRÉCHET SPACES ℓ^p+ AND L^p−
• Composition Semigroups and the Cesàro Operator OnH ^p
• Extension of C ∞ Functions Defined in a Half Space
• On the Uniform Ergodic Theorem
• Remarks on Ergodic Theorems

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