Dynamics of Fourier Multipliers on Riemannian Symmetric Spaces of Noncompact Type

Authors

• Swagato K. Ray, Indian Statistical Institute, Kolkata
• Rudra P. Sarkar, Indian Statistical Institute, Kolkata

Article Type

Research Article

Publication Title

Publications of the Research Institute for Mathematical Sciences

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 < ∞. This vastly generalizes the result that dynamics of the (perturbed) heat semigroup is chaotic on X proved in Ji and Weber (Ergodic Theory Dynam. Systems 30 (2010), 457–468) and Pramanik and Sarkar (J. Funct. Anal. 266 (2014), 2867–2909).

First Page

293

Last Page

313

DOI

10.4171/prims/61-3-1

Publication Date

1-1-2025

Recommended Citation

Ray, Swagato K. and Sarkar, Rudra P., "Dynamics of Fourier Multipliers on Riemannian Symmetric Spaces of Noncompact Type" (2025). Journal Articles. 5318.
https://digitalcommons.isical.ac.in/journal-articles/5318