Singular distributions and symmetry of the spectrum

2013/01/12 by Gady Kozma, Kozma, Gady, Alexander Olevskiı̆ +1
Mathematics · #Advanced Banach Space Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1301.2636

openalex publication_date 2013/01/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is a survey of the "Fourier symmetry" of measures and distributions on the circle in relation with the size of their support. Mostly it is based on our paper arxiv:1004.3631 and a talk given by the second author in the 2012 Abel symposium.

Related

• Singular distributions, dimension of support, and symmetry of Fourier transform
• On the Titchmarsh convolution theorem for distributions on the circle
• Spectral pairs and positive definite tempered distributions
• Obtaining the Fourier spectrum via Fourier coefficients
• Fourier transforms of spherical distributions on compact symmetric spaces