The Logvinenko-Sereda Theorem for the Fourier-Bessel transform

Abstract

The aim of this paper is to establish an analogue of Logvinenko-Sereda's theorem for the Fourier-Bessel transform (or Hankel transform) $\ff_α$ of order $\alpha >-1/2$. Roughly speaking, if we denote by $P{W}_{\alpha }(b)$ the Paley-Wiener space of $L^2$-functions with Fourier-Bessel transform supported in $[0,b]$, then we show that the restriction map $f\to f{|}_{\Omega }$ is essentially invertible on $P{W}_{\alpha }(b)$ if and only if $\Omega$ is sufficiently dense. Moreover, we give an estimate of the norm of the inverse map. As a side result we prove a Bernstein type inequality for the Fourier-Bessel transform.

Cited by in corpus (4)

• An abstract Logvinenko-Sereda type theorem for spectral subspaces
• Scale-free unique continuation estimates and Logvinenko-Sereda Theorems on the torus
• Fourier and Beyond: Invariance Properties of a Family of Integral Transforms
• Sturm-Liouville Problems And Global Bounds By Small Control Sets And applications to quantum graphs