On certain non-unique solutions of the Stieltjes moment problem

Details On certain non-unique solutions of the Stieltjes moment problem On certain non-unique solutions of the Stieltjes moment problem

2009-09-26

arxiv.org/abs/0909.4846v1

Mathematics

Functional Analysis

Scientific paper

We construct explicit solutions of a number of Stieltjes moment problems based on moments of the form ${\rho}_{1}^{(r)}(n)=(2rn)!$ and ${\rho}_{2}^{(r)}(n)=[(rn)!]^{2}$, $r=1,2,...$, $n=0,1,2,...$, \textit{i.e.} we find functions $W^{(r)}_{1,2}(x)>0$ satisfying $\int_{0}^{\infty}x^{n}W^{(r)}_{1,2}(x)dx = {\rho}_{1,2}^{(r)}(n)$. It is shown using criteria for uniqueness and non-uniqueness (Carleman, Krein, Berg, Pakes, Stoyanov) that for $r>1$ both ${\rho}_{1,2}^{(r)}(n)$ 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 generalizing ${\rho}_{1,2}^{(r)}(n)$, such as the product ${\rho}_{1}^{(r)}(n)\cdot{\rho}_{2}^{(r)}(n)$ and $[(rn)!]^{p}$, $p=3,4,...$.

Affiliated with

Also associated with

No associations

Rating

On certain non-unique solutions of the Stieltjes moment problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On certain non-unique solutions of the Stieltjes moment problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On certain non-unique solutions of the Stieltjes moment problem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-155538