Continuous frames and the Kadison-Singer problem

2018/02/01 by Bownik, Marcin · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1802.00118

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.

Cited by

• Frame redundancy and Beurling density

Related

• Lyapunov's Theorem for continuous frames
• The Kadison-Singer Problem
• The discretization problem for continuous frames
• Continuous Frames, Function Spaces, and the Discretization Problem
• Continuous frames in Krein spaces