On the xth root of a Stieltjes moment sequence

[摘要] Stieltjes moment sequences {a(n)}(n=0)(infinity) whose xth roots {x root a(n)}(n=0)(infinity) are Stieltjes moment sequences are studied (x is a fixed integer greater than or equal to 2).A formula connecting the closed supports of representing measures of {a(n)}(n=0)(infinity) and {x root a(n)}(n=0)(infinity) 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, infinity) of cardinality M and N, respectively, is described. (C) 2012 Elsevier Inc. All rights reserved.

[发布日期] 2012-12-15

[关键词] Stieltjes moment sequence;xth root of a Stieltjes moment sequence;Representing measure;Support of a measure;Hole of a support