In this talk, we will try to characterize eigenfunctions of the Laplaceâ€“Beltrami operator using Fourier multipliers via Roe-Strichartz type theorems in rank one symmetric spaces of noncompact type. This work has its origin in a simple result of Roe, which says that if all the derivatives and antiderivatives of a given function on the real line are uniformly bounded, then the function is a linear combination of sin(x) and cos(x). We will talk about ramification of this result in context of characterizing eigenfunctions of the Laplace-Beltrami operator. The talk will be based on a joint work with Prof. Rudra P. Sarkar.

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Last updated: 13 Jun 2024