Bulletin of the Belgian Mathematical Society - Simon Stevin

Dynamics of multidimensional Cesáro operators

J. Alberto Conejero, A. Mundayadan, and J.B. Seoane-Sepúlveda

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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.

Article information

Bull. Belg. Math. Soc. Simon Stevin, Volume 26, Number 1 (2019), 11-20.

First available in Project Euclid: 20 March 2019

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A16: Cyclic vectors, hypercyclic and chaotic operators 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
Secondary: 47B38: Operators on function spaces (general) 47B99: None of the above, but in this section

Cesáro integral operator frequent hypercyclicity hypercyclic operator Linear Dynamics


Alberto Conejero, J.; Mundayadan, A.; Seoane-Sepúlveda, J.B. Dynamics of multidimensional Cesáro operators. Bull. Belg. Math. Soc. Simon Stevin 26 (2019), no. 1, 11--20. doi:10.36045/bbms/1553047226. https://projecteuclid.org/euclid.bbms/1553047226

Export citation