Singular measure with tiny Fourier spectrum on three dimensional sphere

Wed, 13-Nov-2025 

Abstract

I will present a construction of a singular measure on three dimensional sphere S^3 whose non-zero components in spherical harmonic decomposition are concentrated around lines y=ax and x=ay. This could be seen as a generalization of Aleksandrov's singular pluriharmonic measure or an inverse to the Brummelhuis condition of absolute continuity. The main ingredient is  a construction of bounded spherical harmonics with small, localized Fourier spectra.