# On truncated and full classical Markov moment problems

@inproceedings{Olteanu2021OnTA, title={On truncated and full classical Markov moment problems}, author={Octav Olteanu}, year={2021} }

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 ≤ p <∞) spaces setting, is the first aim of this work. Reduced (truncated) moment problems arise in real-world situations, where only a finite number of samples are available. We obtain solutions as nonnegative functions in a Lq,μ (S) space, where S ⊂ R is a closed subset, μ is a regular Borel…

## 3 Citations

On Markov Moment Problem and Related Results

- MathematicsSymmetry
- 2021

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 the Moment Problem and Related Problems

- MathematicsMathematics
- 2021

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…

On Hahn-Banach theorem and some of its applications

- MathematicsOpen Mathematics
- 2022

Abstract First, this work provides an overview of some of the Hahn-Banach type theorems. Of note, some of these extension results for linear operators found recent applications to isotonicity of…

## References

SHOWING 1-10 OF 30 REFERENCES

Polynomial Approximation on Unbounded Subsets, Markov Moment Problem and Other Applications

- Mathematics
- 2020

This paper starts by recalling the author’s results on polynomial approximation over a Cartesian product A of closed unbounded intervals and its applications to solving Markov moment problems. Under…

SOME NEW ASPECTS OF THE L-MOMENT PROBLEM

- Mathematics
- 2010

This note is devoted to the L-moment problem. The L-moment problem consists of characterising the sequence of moments an = ∫ Rt nf(t)dt, n ∈ N of a real measurable function f (with prescribed…

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

- Mathematics
- 2020

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…

An operator-valued moment problem

- Mathematics
- 1991

We link Carey's exponential representation of the determining function of a perturbation pair with the moment problem. We prove that an operator sequence represents the moments of a phase operator if…

A remark on the multidimensional moment problem

- Mathematics
- 1979

To mot ivate the following results let us recall some definitions and results with relation to the m o m e n t problem. Let (S, + ) be an abelian semigroup with neutral element 0. A real-valued…

The fixed point for a transformation of Hausdorff moment sequences and iteration of a rational function

- Mathematics
- 2007

We study the fixed point for a non-linear transformation in the set of Hausdorffmoment sequences,
defined by the formula: T ((an))n = 1/(a0+�E �E �E+an).We determine the corresponding measure�E,…

Ordered vector spaces and linear operators

- Mathematics
- 1976

An ordered vector space is just that-a set with both a (real) vector space structure and an order relation which satisfy desirable compatibility conditions. Specialization by requiring that the least…

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

- MathematicsSIAM J. Appl. Math.
- 2008

A constructive algorithm is presented to solve the moment problems numerically and it is proved that the algorithm computes the right solution.

On the moment problem

- Mathematics
- 2002

The purpose of this paper is to provide some additional insight into the moment problem by connecting a condition by Lin, Bondesson's class of hyperbolically completely monotone densities, and the…

From the Hahn–Banach extension theorem to the isotonicity of convex functions and the majorization theory

- MathematicsRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
- 2020

The property of isotonicity of a continuous convex function on the positive cone is characterized via subdifferentials. This is used to illustrate a new generalization of the Hardy–Littlewood–Polya…