Hausdorff dimension and distance sets
Copyright policy )Hausdorff dimension and distance sets
The author uses a brilliant refinement of Fourier restriction phenomena to spheres to improve results on difference sets \(D(A)= \{| x- y|; x,y\in A\}\) for Souslin sets \(A\) in \(\mathbb{R}^ n\) due to Falconer. For example, if \(A\subset \mathbb{R}^ 2\) and the Hausdorff dimension \(\dim A> {13\over 9}\) (instead of \({3\over 2}\) as in Falconer's general result) then \(D(A)\) has positive measure.
Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions, Hausdorff and packing measures, Fourier transform, Hausdorff dimension, Fourier restriction phenomena, difference sets
Almost periodic functions on groups and semigroups and their generalizations (recurrent functions, distal functions, etc.); almost automorphic functions, Hausdorff and packing measures, Fourier transform, Hausdorff dimension, Fourier restriction phenomena, difference sets
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).30 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!