Spectral concentration of positive functions on compact groups (Q719698)

It is well known that quadrature rules are basic tools for numerical integration and can be related in a variety of settings. The authors only require that the quadrature rules have positive weights and they prefer rules with small simple sets. The focus of the paper is to give a probabilistic (nonconstructive) proof for the existence of quadrature rules that apply to any band limit on any compact group. The authors construct new quadrature rules and prove lower bands on their maximum weights. Finally, these rules are applied to prove a spectral concentration theorem for band-limited positive functions (this is the main result of the paper).