# Approximation and Markov moment problem on concrete spaces

@article{Olteanu2014ApproximationAM, title={Approximation and Markov moment problem on concrete spaces}, author={Octav Olteanu}, journal={Rendiconti del Circolo Matematico di Palermo (1952 -)}, year={2014}, volume={63}, pages={161-172} }

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 vector valued moment problems in terms of quadratic mappings. Two other applications related to the Markov moment problem are considered. The main ingredients of the proofs are the extension of linear operator’s results, with two constraints. All sections contain statements using Hahn–Banach principle…

## 10 Citations

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

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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…

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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.

### Markov Moment Problem in Concrete Spaces Revisited

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This review paper starts by recalling two main results on abstract Markov moment problem. Corresponding applications to problems involving concrete spaces of functions and self-adjoint operators are…

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

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- 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…

### Markov Moment Problem and Related Approximation

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- 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…

### New Results on Extension of Linear Operators and Markov Moment Problem

- Mathematics
- 2020

One recalls earlier applications of extension of linear operators with two constraints to the abstract Markov moment problem and Mazur-Orlicz theorem. Next we generalize one of our previous results…

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- 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…

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- 2014

The present work deals with optimization in kinematics, generalizing previous results of the author. A second theme is maximizing the constrained gain linear function and minimizing the constrained…

### EXTENSION AND DECOMPOSITION OF LINEAR OPERATORS DOMINATED BY CONTINUOUS INCREASING SUBLINEAR OPERATORS

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We point out new applications of earlier results on constrained extension of linear operators. In section 2, similar results with respect to previous ones on the Riesz decomposition property, but now…

### POLYNOMIAL APROXIMATION ON UNBOUNDED SETS AND THE MULTIDIMENSIONAL MOMENT PROBLEM

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- 2015

We solve a two dimensional moment problem on a space of absolutely integrable functions in a strip. To this end, we approximate nonnegative continuous compactly supported functions by sums of tensor…

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