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.
Additional Metadata
Keywords Truncated moment problem, Hankel matrix, flat extension, moment matrix, polynomial optimization
THEME Logistics (theme 3)
Publisher Birkhäuser
Journal Archiv der Mathematik = Archives of Mathematics
Laurent, M, & Mourrain, B. (2009). A generalized flat extension theorem for moment matrices. Archiv der Mathematik = Archives of Mathematics, 93(1), 87–98.