Time: Tuesday, December 8, 2015
2:00pm
MTH1311

Speaker: Professor Yeonhyang Kim (Central Michigan University)

Title: Minimal scalings and scalable frames

Abstract: It is known that the set of all scalings of a scalable frame F is a convex polytope with vertices corresponding minimal scalings. In this talk, we provide a method to find a subset of contact points which provides a decomposition of the identity, and an estimate of the number of minimal scalings of a scalable frame. We provide a characterization of when minimal scalings are affinely dependent. Using this characterization, we can conclude that all strict scalings of F have the same structural property. We also present the uniqueness of orthogonal partitioning property of any set of minimal scalings, which provides all possible tight subframes of a given scaled frame.