Mathematics – Functional Analysis
Scientific paper
2012-04-07
Mathematics
Functional Analysis
To appear in J. Operator Theory
Scientific paper
A theorem of Bayer and Teichmann implies that if a finite real multisequence \beta = \beta^(2d) has a representing measure, then the associated moment matrix M_d admits positive, recursively generated moment matrix extensions M_(d+1), M_(d+2),... For a bivariate recursively determinate M_d, we show that the existence of positive, recursively generated extensions M_(d+1),...,M_(2d-1) is sufficient for a measure. Examples illustrate that all of these extensions may be required to show that \beta has a measure. We describe in detail a constructive procedure for determining whether such extensions exist. Under mild additional hypotheses, we show that M_d admits an extension M_(d+1) which has many of the properties of a positive, recursively generated extension.
Curto Raul E.
Fialkow Lawrence A.
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