Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited

We prove a Cauchy identity for free quasi-symmetric functions and apply it to the study of various bases. A free Weyl formula and a generalization of the splitting formula are also discussed.Comment: 21 pages, Latex, 2 figure

On certain non-unique solutions of the Stieltjes moment problem

We construct explicit solutions of a number of Stieltjes moment problems based on moments of the form (2rn)! and [(rn)!]2. It is shown using criteria for uniqueness and non-uniqueness (Carleman, Krein, Berg, Pakes, Stoyanov) that for r > 1 both forms give rise to non-unique solutions. Examples of such solutions are constructed using the technique of the inverse Mellin transform supplemented by a Mellin convolution. We outline a general method of generating non-unique solutions for moment problems

Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited

21 pages, Latex, 2 figuresInternational audienceWe prove a Cauchy identity for free quasi-symmetric functions and apply it to the study of various bases. A free Weyl formula and a generalization of the splitting formula are also discussed

Noncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited

21 pages, Latex, 2 figuresInternational audienceWe prove a Cauchy identity for free quasi-symmetric functions and apply it to the study of various bases. A free Weyl formula and a generalization of the splitting formula are also discussed