# On Markov Moment Problem and Mazur-Orlicz Theorem

@article{Olteanu2017OnMM, title={On Markov Moment Problem and Mazur-Orlicz Theorem}, author={Octav Olteanu and Janina Mihaela Mihăilă}, journal={Open Access Library Journal}, year={2017}, volume={4}, pages={1-10} }

Applications of the generalization of Mazur-Orlicz theorem to concrete spaces are proved. Suitable moment problems are solved, as applications of extension theorems of linear operators with a convex and a concave constraint. In particular, a relationship between Mazur-Orlicz theorem and Markov moment problem is partially illustrated. In the end of this work, an application to the multidimensional Markov moment problem of an earlier extension result on a distanced subspace with respect to a…

## 2 Citations

Extension of Linear Operators and Polynomial Approximation, with Applications to Markov Moment Problem and Mazur-Orlicz Theorem

- Mathematics
- 2019

One recalls the relationship between the Markov moment problem and extension of linear functionals (or operators), with two constraints. One states necessary and sufficient conditions for the…

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…

## References

SHOWING 1-10 OF 21 REFERENCES

APPLICATIONS OF EXTENSION THEOREMS OF LINEAR OPERATORS TO MAZUR-ORLICZ AND MOMENT PROBLEMS

- Mathematics
- 2014

The aim of the present work is to give applications to concrete spaces of functions and operators of some theorems of extension of linear operators, with two constraints. Constrained interpolation…

Markov Moment Problem and Related Approximation

- Mathematics
- 2013

The present review article contains recently published results on Markov moment problem and related approximation. The main idea is to apply theorems concerning solutions of the abstract moment…

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…

Hardy's Condition in the Moment Problem for Probability Distributions

- Mathematics
- 2013

In probabilistic terms Hardy's condition is written as follows: ${\bf E}\,[e^{c{\sqrt X}}] 0$ a constant. If this holds, then all moments of $X$ are finite and the distribution of $X$ is uniquely…

Application de théorèmes de prolongement d'opérateurs linéaires au problème des moments et à une généralisation d'un théorème de Mazur-Orlicz

- Mathematics
- 1991

Dans cette Note nous appliquons les theoremes generaux [13], th. 2, p. 514 et [14], th. I. 1, p. 956; th. I. 3, p. 963, aux problemes abstraits et classiques des moments, et aussi a un theoreme de…

New Results on Markov Moment Problem

- Mathematics
- 2013

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 Some Basic Theorems in Convex Analysis

- Modern Applied Mathematics—Optimization and Operations Research,
- 1982

Operator-Valued Mazur-Orlicz and Moment Problems in Spaces of Analytic Function

- UPB Scientific Bulletin, Series A,
- 2017