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march 2019 Dynamics of multidimensional Cesáro operators
J. Alberto Conejero, A. Mundayadan, J.B. Seoane-Sepúlveda
Bull. Belg. Math. Soc. Simon Stevin 26(1): 11-20 (march 2019). DOI: 10.36045/bbms/1553047226

Abstract

We study the dynamics of the multi-dimensional Ces\`aro integral operator on $L^p(I^n)$, for $I$ the unit interval, $1<p<\infty$, and $n\ge 2$, that is defined as \begin{multline*} \displaystyle \mathcal{C}(f)(x_1,\ldots,x_n)=\frac {1} {x_1x_2\cdots x_n} \int_0^{x_1}\ldots\int_{0}^{x_n} f(u_1,\ldots,u_n)du_1\ldots du_n\\ \quad \text{ for } f\in L^p(I^n). \end{multline*} This operator is already known to be bounded. As a consequence of the Eigenvalue Criterion, we show that it is hypercyclic as well. Moreover, we also prove that it is Devaney chaotic and frequently hypercyclic.

Citation

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J. Alberto Conejero. A. Mundayadan. J.B. Seoane-Sepúlveda. "Dynamics of multidimensional Cesáro operators." Bull. Belg. Math. Soc. Simon Stevin 26 (1) 11 - 20, march 2019. https://doi.org/10.36045/bbms/1553047226

Information

Published: march 2019
First available in Project Euclid: 20 March 2019

zbMATH: 07060313
MathSciNet: MR3934078
Digital Object Identifier: 10.36045/bbms/1553047226

Subjects:
Primary: 47A16, 47B37
Secondary: 47B38, 47B99

Rights: Copyright © 2019 The Belgian Mathematical Society

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Vol.26 • No. 1 • march 2019
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