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What is Cantor Construction of Salem Sets about?

This document summarizes a theorem by Christian Bluhm on constructing linear fractal Salem sets through a deterministic Cantor-type construction. The construction involves recursively choosing integers Mk based on a parameter α to define a set Sα as the intersection of intervals defined by the primes p in the ranges PMk. A measure μα supported on Sα is then constructed such that its Fourier transform decays like (1+|x|)-1/(2+α), showing Sα is a Salem set of dimension 2/(2+α).

Author

Anonymous UrVkcd

Language

EN