Continuous frames and the Kadison-Singer problem

Abstract

In this paper we survey a recent progress on continuous frames inspired by the solution of the Kadison-Singer problem by Marcus, Spielman, and Srivastava. We present an extension of Lyapunov's theorem for discrete frames due to Akemann and Weaver and a similar extension for continuous frames by the author. We also outline a solution of the discretization problem, which was originally posed by Ali, Antoine, and Gazeau, and recently solved by Freeman and Speegle.