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arXiv · 2508.19975

Expansivity and shadowing for composition operators on Paley-Wiener spaces

Carlos F. Álvarez·O. R. Severiano
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Abstract

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

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Carlos F. Álvarez, O. R. Severiano. 2025-08-27. Expansivity and shadowing for composition operators on Paley-Wiener spaces. https://arxiv.org/abs/2508.19975

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