# New Results on Markov Moment Problem

@article{Olteanu2013NewRO, title={New Results on Markov Moment Problem}, author={Octav Olteanu}, journal={International Journal of Analysis}, year={2013}, volume={2013}, pages={1-17} }

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 background containing applications of extension results of linear operators with two constraints to the moment problem and approximation by polynomials on unbounded closed finite-dimensional subsets. Two domain spaces are considered: spaces of absolute integrable functions and spaces of analytic functions…

## 19 Citations

Approximation and Markov moment problem on concrete spaces

- Mathematics
- 2014

Polynomial approximation results on unbounded subsets of $$R^n$$Rn are discussed. By applying these results, one obtains characterizations of the existence of the solutions of the multidimensional…

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…

Markov moment problem and approximation

- Mathematics
- 2014

In this paper, we start by recalling some polynomial approximation results on unbounded subsets of Rn. Namely one approximates nonnegative continuous functions with compact support by sums of tensor…

On Markov Moment Problem and Related Inverse Problems

- Mathematics
- 2019

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…

Approximation on unbounded subsets and the moment problem

- Mathematics
- 2014

We apply L 1 approximation to characterize existence of the solutions of the multidimensional moment problems in terms of quadratic mappings, similarly to the one-dimensional case. To this end, we…

On Markov Moment Problem and Mazur-Orlicz Theorem

- Mathematics
- 2017

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…

Optimization related to the Markov moment problem and bounds concerning Newton’s method for operators

- Mathematics
- 2014

The first aim of this work is to give necessary and sufficient conditions on the existence of a Markov moment problem in the first quadrant in terms of quadratic forms. This allows establishing the…

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…

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…

MAZUR-ORLICZ THEOREM IN CONCRETE SPACES AND INVERSE PROBLEMS RELATED TO THE MOMENT PROBLEM

- Mathematics
- 2017

In the first part of this work, we derive some new applications of a version of Mazur-Orlicz theorem, in concrete spaces of absolutely integrable functions and respectively continuous functions of…

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