A note on the Fourier transform of fractal measures

DOI10.4310/MRL.2004.v11.n3.a3zbMath1083.42006OpenAlexW2170213212MaRDI QIDQ1890229

Mehmet Burak Erdogan

Publication date: 29 December 2004

Published in: Mathematical Research Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4310/mrl.2004.v11.n3.a3

zbMATH Keywords

distance set problemenergy of a measureFourier transform of a measureStein-Tomas restriction theorem

Mathematics Subject Classification ID

Contents, measures, outer measures, capacities (28A12) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Conformal densities and Hausdorff dimension for holomorphic dynamical systems (37F35) Length, area, volume, other geometric measure theory (28A75) Fractals (28A80)

Related Items (21)

On Falconer's distance set conjecture ⋮ On the asymptotics of the Hopf characteristic function ⋮ Pointwise convergence of sequential Schrödinger means ⋮ Weighted Fourier extension estimates and applications ⋮ Fourier decay of fractal measures on surfaces of co-dimension two in \(\mathbb{R}^5\) ⋮ A family of fractal Fourier restriction estimates with implications on the Kakeya problem ⋮ A NOTE ON LOCALISED WEIGHTED INEQUALITIES FOR THE EXTENSION OPERATOR ⋮ Exceptional sets of projections, unions of \(k\)-planes and associated transforms ⋮ Average decay of the Fourier transform of measures with applications ⋮ Fourier decay of fractal measures on hyperboloids ⋮ Application of a Fourier restriction theorem to certain families of projections in \(\mathbb R^3\) ⋮ Averaged decay estimates for Fourier transforms of measures over curves with nonvanishing torsion ⋮ Fractal Strichartz estimate for the wave equation ⋮ Dimension of divergence set of the wave equation ⋮ On exact statistics and classification of ergodic systems of integer dimension ⋮ Improved decay of conical averages of the Fourier transform ⋮ Hausdorff dimension and projections related to intersections ⋮ Fourier restriction in low fractal dimensions ⋮ Packing spheres and fractal Strichartz estimates in $\mathbb {R}^d$ for $d\geq 3$ ⋮ Localisation of Bochner Riesz means on sets of positive Hausdorff dimension in \mathbb{R}^d ⋮ Improved bounds for restricted projection families via weighted Fourier restriction

This page was built for publication: A note on the Fourier transform of fractal measures