Abstract
Stieltjes moment sequences {an}n=0∞ whose ϰth roots {anϰ}n=0∞ are Stieltjes moment sequences are studied (ϰ is a fixed integer greater than or equal to 2). A formula connecting the closed supports of representing measures of {an}n=0∞ and {anϰ}n=0∞ is established. The relationship between the holes of the supports of these measures is investigated. The set of all pairs (M,N) of positive integers for which there exists a Stieltjes moment sequence whose square root is a Stieltjes moment sequence and both of them have representing measures supported on subsets of (0,∞) of cardinality M and N, respectively, is described.
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