Existence, Uniqueness, and a Constructive Solution Algorithm for a Class of Finite Markov Moment Problems

@article{Gosse2008ExistenceUA,
  title={Existence, Uniqueness, and a Constructive Solution Algorithm for a Class of Finite Markov Moment Problems},
  author={Laurent Gosse and Olof Runborg},
  journal={SIAM J. Appl. Math.},
  year={2008},
  volume={68},
  pages={1618-1640}
}
We consider a class of finite Markov moment problems with an arbitrary number of positive and negative branches. We show criteria for the existence and uniqueness of solutions, and we characterize in detail the nonunique solution families. Moreover, we present a constructive algorithm to solve the moment problems numerically and prove that the algorithm computes the right solution. 
View PDF on arXiv
15 Citations
Highly Influential Citations
2
Background Citations
6
Methods Citations
2
Results Citations
2

15 Citations

On Markov Moment Problem and Related Inverse Problems

We give necessary and sufficient conditions for the existence of a unique solution of a multidimensional real classical Markov moment problem, in terms of quadratic forms. Next, we consider…

New Results on Markov Moment Problem

The present work deals with the existence of the solutions of some Markov moment problems. Necessary conditions, as well as necessary and sufficient conditions, are discussed. One recalls the…

On Markov Moment Problem and Related Results

TLDR
New results and theorems on the vector-valued Markov moment problem are proved by means of polynomial approximation on unbounded subsets, also applying an extension of the positive linear operators’ result.

On Special Properties for Continuous Convex Operators and Related Linear Operators

This paper provides a uniform boundedness theorem for a class of convex operators, such as Banach–Steinhaus theorem for families of continuous linear operators. The case of continuous symmetric…

New Results onMarkovMoment Problem

e present work deals with the existence of the solutions of some Markov moment problems. Necessary conditions, as well as necessary and sufficient conditions, are discussed. One recalls the…

On truncated and full classical Markov moment problems

Abstract Giving necessary and sufficient conditions for the existence of solutions of truncated and full classical Markov moment problems in terms of the given (or measured) moments, in Lp,μ (S) (1 ≤…

On the Moment Problem and Related Problems

Firstly, we recall the classical moment problem and some basic results related to it. By its formulation, this is an inverse problem: being given a sequence (yj)j∈ℕn  of real numbers and a closed…

From Hahn–Banach Type Theorems to the Markov Moment Problem, Sandwich Theorems and Further Applications

The aim of this review paper is to recall known solutions for two Markov moment problems, which can be formulated as Hahn–Banach extension theorems, in order to emphasize their relationship with the…

Almost power sum systems

TLDR
For the system with even power gaps the obtained equalities are the analogs of Newton’s identities, which express the connection between elementary symmetric functions and odd power sums.

Solving composite sum of powers via Padé approximation and orthogonal polynomials with application to optimal PWM problem

  • P. Kujan
  • Mathematics, Computer Science
    Appl. Math. Comput.
  • 2014

References

SHOWING 1-10 OF 29 REFERENCES

Resolution of the finite Markov moment problem

TIME OPTIMALITY AND THE POWER MOMENT PROBLEM

A solution of the problem of exact determination of a time optimal control for the equation , in the open loop form as well as in the closed loop form is presented in this paper. A system of special…

The Classical Moment Problem as a Self-Adjoint Finite Difference Operator

Abstract This is a comprehensive exposition of the classical moment problem using methods from the theory of finite difference operators. Among the advantages of this approach is that the Nevanlinna…

The Markov moment problem and de Finetti’s theorem: Part II

Abstract.This paper gives an abstract version of de Finetti’s theorem that characterizes mixing measures with Lp densities. The general setting is reviewed; after the theorem is proved, it is…

The Markov moment problem and de Finetti’s theorem: Part I

Abstract.The Markov moment problem is to characterize sequences admitting the representation sn=∫01xnf(x)dx, where f(x) is a probability density on [0,1] and 0≤f(x)≤c for almost all x. There are…

Recovering a function from a finite number of moments

TLDR
The problem of recovering a function from its moments for the case of a finite number of data contaminated by noise is considered and a stability theorem and an algorithm are presented.

The Markov power moment problem in problems of controllability and frequency extinguishing for the wave equation on a half-axis

A kinetic formulation for multi-branch entropy solutions of scalar conservation laws

Superresolution in the Markov Moment Problem

Abstract Suppose that \bar x is a characteristic function and a 1 ,  a 2 ,…,  a n are weight functions on a finite measure space. Recent work of Gamboa and Gassiat observed conditions guaranteeing…

Finite Moment Problems and Applications to Multiphase Computations in Geometric Optics

Recovering a function out of a finite number of moments is generally an ill-posed inverse problem. We focus on two special cases arising from applications to multiphase geometric optics computations…