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.
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Birkhäuser
Archiv der Mathematik = Archives of Mathematics
Networks and Optimization

Laurent, M., & Mourrain, B. (2009). A generalized flat extension theorem for moment matrices. Archiv der Mathematik = Archives of Mathematics, 93(1), 87–98.