Recursively determined representing measures for bivariate truncated moment sequences

A theorem of Bayer and Teichmann [BT] implies that if a finite real multisequence (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 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.