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arXiv · 1805.10048

Chaotic behaviour of the Fourier multipliers on Riemannian symmetric spaces of noncompact type

Swagato K. Ray·Rudra P. Sarkar
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Abstract

Let $X$ be a Riemannian symmetric space of noncompact type and $T$ be a linear translation-invariant operator which is bounded on $L^p(X)$. We shall show that if $T$ is not a constant multiple of identity then there exist complex constants $z$ such that $zT$ is chaotic on $L^p(X)$ when $p$ is in the sharp range $2<p<\infty$. This vastly generalizes the result that dynamics of the (perturbed) heat semigroup is chaotic on $X$ proved in [15, 17].

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Swagato K. Ray, Rudra P. Sarkar. 2018-05-25. Chaotic behaviour of the Fourier multipliers on Riemannian symmetric spaces of noncompact type. https://arxiv.org/abs/1805.10048

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