In this note we prove a generalization of the flat extension theorem of Curto and Fialkow [4] for truncated moment matrices. It applies to moment matrices indexed by an arbitrary set of monomials and its border, assuming that this set is connected to 1. When formulated in a basis-free setting, this gives an equivalent result for truncated Hankel operators.
Truncated moment problem, Hankel matrix, flat extension, moment matrix, polynomial optimization
Logistics (theme 3)
Cornell University Library e-Print archive
Semidefinite programming and combinatorial optimization
Networks and Optimization

Laurent, M, & Mourrain, B. (2008). A sparse flat extension theorem for moment matrices. e-Print archive. Cornell University Library .