Recursively determined representing measures for bivariate truncated moment sequences

Raul E. Curto; Lawrence A. Fialkow

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arXiv · 1204.1687

Recursively determined representing measures for bivariate truncated moment sequences

Raul E. Curto·Lawrence A. Fialkow

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Abstract

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.

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BibTeX RIS

Raul E. Curto, Lawrence A. Fialkow. 2012-04-07. Recursively determined representing measures for bivariate truncated moment sequences. https://arxiv.org/abs/1204.1687

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