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Let $\gamma ^{\left( n\right) }\equiv \{\gamma _{ij}\}\,(0\leq i+j\leq 2n,\,|i-j|\leq n)$ be a sequence in the complex number set $\mathbb{C}$ and let $E\left( n\right) $ be the Embry truncated moment matrices corresponding from $\gamma ^{\left( n\right) }$. For an odd number $n$, it is known that $ \gamma ^{\left( n\right) }$ has a rank $E\left( n\right) $\textit{-}atomic representing measure if and only if $E(n)\geq 0$ and $E(n)$ admits a flat extension $E(n+1)$. In this paper we suggest a related problem: if $E(n)$ is positive and nonsingular, does $E(n)$ have a flat extension $E(n+1)$? and give a negative answer in the case of $E(3)$. And we obtain some necessary conditions for positive and nonsingular matrix $E\left( 3\right)$, and also its sufficient conditions.
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참고문헌 (11)
참고문헌 신청
R. E. Curto / 1996 / Solution of the truncated complex moment problem for at data / Mem. Amer. Math. Soc 119(5):68
R. E. Curto / 1998 / Flat extensions of positive moment matrices: recursively generated relations / Mem. Amer. Math. Soc. 136(648):x+56
R. E. Curto / 2002 / Solution of the singular quartic moment problem / J. Operator Theory 48(2):315~354
R. E. Curto / 1998 / Nonselfadjoint operator algebras, operator theory, and related topics / Birkhauser :59~82
L. Fialkow / 1995 / Multivariable operator theory (Seattle, WA, 1993) / Amer. Math. Soc. :133~150
R. E. Curto / 1998 / Flat extensions of positive moment matrices: recursively generated relations / Mem. Amer. Math. Soc. 136(648):x+56
R. E. Curto / 2002 / Solution of the singular quartic moment problem / J. Operator Theory 48(2):315~354
R. E. Curto / 1998 / Nonselfadjoint operator algebras, operator theory, and related topics / Birkhauser :59~82
L. Fialkow / 1995 / Multivariable operator theory (Seattle, WA, 1993) / Amer. Math. Soc. :133~150
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