Restricting Fourier transforms of measures to curves in R^2
M. Burak Erdogan, Daniel M. Oberlin
TL;DR
This paper develops estimates for the restriction of Fourier transforms of fractal measures to specific curves in R^2, advancing understanding of Fourier analysis on fractal sets.
Contribution
It introduces new restriction estimates for Fourier transforms of fractal measures when restricted to certain curves in the plane.
Findings
Established restriction estimates for Fourier transforms of fractal measures on curves in R^2.
Extended Fourier restriction theory to fractal measures with specific geometric properties.
Provided new bounds that could impact analysis of fractal sets and harmonic analysis.
Abstract
We establish estimates for restrictions to certain curves in R^2 of the Fourier transforms of some fractal measures.
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Taxonomy
TopicsMathematical Dynamics and Fractals · advanced mathematical theories · Advanced Harmonic Analysis Research