Localization of orthonormal sequences in the spherical mean setting (Q305836)

The authors summarize the contents of this paper in the introduction of the paper as follows: The aim of this work is to prove a generalized quantitative version of the mean-dispersion Shapiro's theorem associated with the spherical mean operator. We recall some harmonic analysis results related to the spherical mean operator and its Fourier transform. Then we will prove first a generalized quantitative version of the mean-dispersion Shapiro's theorem, next we will obtain one multiplicative form of this theorem for orthonormal basis.