A Gröbner Basis Proof of the Flat Extension Theorem for Moment Matrices
نویسنده
چکیده
Curto and Fialkow proved in 1996 that flat positive semidefinite moment matrices always come from a finitely atomic positive measure. The tedious part of the proof is to show that flat moment matrices have always a flat extension. We give a new short argument for this based on Gröbner bases. Résumé. Curto et Fialkow ont démontré en 1996 que les matrices des moments, plates et semidéfinies positives, proviennent d’une mesure positive d’un nombre fini d’atomes. La partie ardue de la preuve consiste à démontrer que les matrices des moments plates admettent toujours une extension plate. Nous donnons un nouvel argument pour cela qui est fondé sur les bases de Gröbner.
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