Codes and Expansions (CodEx) Seminar

Radu Balan (University of Maryland):
Factorization of positive-semidefinite operators with absolutely summable entries

A problem by Feichtinger, Heil, and Larson asks whether a positive-semidefinite integral operator with M1 kernel admits a symmetric rank-one decomposition which is strongly square-summable with respect to the M1 norm. In conjunction with a concurrent result by Bandeira-Mixon-Steinerberger, we provide a negative answer to the problem and study special cases where such factorization is possible. We also discuss an application of the results to the semidefinite relaxation of certain quadratic programs. This talk is based on joint work with Fushuai (Black) Jiang, arXiv:2409.20372.