Speaker: Michal Wojciechowski (Institute of Mathematics of the Polish Academy of Sciences)

Title: Singular measure with tiny Fourier spectrum on three dimensional sphere

Abstract: I will present a construction of a singular measure on three dimensional sphere 𝑆³ 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.