Expansivity and shadowing for composition operators on Paley-Wiener spaces

Abstract

In this article, we study composition operators $C_{\ddot{I}}•f=f\circ \ddot{I}•$ on the full range of Paley-Wiener spaces $B_a^2$ for $a>0.$ Here we compute the spectrum and the spectral radius of $C_{\ddot{I}}•$ on $B_a^2.$ The spectrum of $C_{\ddot{I}}•$ and the location of the fixed point of $\ddot{I}•$ play a fundamental role in our analysis to show that no Paley-Wiener space $B_a^2$ supports composition operators possessing the positive shadowing property. We also provide a complete classification of the composition operators on $B_a^2$ that are positively expansive and absolutely Cesà ro bounded. As a consequence of these results we show that no Paley-Wiener space $B_a^2$ supports Li-Yorke chaotic composition operators.