Fourier transform and expanding maps on Cantor sets
Tuomas Sahlsten, Connor Stevens
Abstract
abstract: We study the Fourier transforms $\widehat{\mu}(\xi)$ of non-atomic Gibbs measures $\mu$ for uniformly expanding maps $T$ of bounded distortions on $[0,1]$ or Cantor sets with strong separation. When $T$ is totally non-linear, then $\widehat{\mu}(\xi)\to 0$ at a polynomial rate as $|\xi|\to\infty$.
Topics & Concepts
Fourier transformFourier analysisMathematicsMathematical analysisMathematical Dynamics and Fractalsadvanced mathematical theoriesMathematical Analysis and Transform Methods