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}
}
  • Octav Olteanu
  • Published 3 February 2013
  • Mathematics
  • International Journal of Analysis
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… 
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19 Citations
Background Citations
7
Methods Citations
3
Results Citations
3

19 Citations

Approximation and Markov moment problem on concrete spaces
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…
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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
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On Markov Moment Problem and Related Inverse Problems
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Approximation on unbounded subsets and the moment problem
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On Markov Moment Problem and Mazur-Orlicz Theorem
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
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
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
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
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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References

SHOWING 1-10 OF 14 REFERENCES
MARKOV-TYPE AND OPERATOR-VALUED MULTIDIMENSIONAL MOMENT PROBLEMS, WITH SOME APPLICATIONS
In Section 2 we prove a general result which gives sufficient conditions for the existence of a solution for a Markov-type moment problem in the space Lν(T ) (the implication (b)⇒ (a) of Theorem…
EXTENSION OF LINEAR OPERATORS, DISTANCED CONVEX SETS AND THE MOMENT PROBLEM
One applies an extension theorem of linear operators ((10, Theorem 5, p. 969)) to the classical moment problem in spaces of continuous functions on a compact interval and in spaces of analytic…
Existence, Uniqueness, and a Constructive Solution Algorithm for a Class of Finite Markov Moment Problems
TLDR
A constructive algorithm is presented to solve the moment problems numerically and it is proved that the algorithm computes the right solution.
Resolution of the finite Markov moment problem
Multivariate distributions and the moment problem
Topological Vector Spaces
This chapter presents the most basic results on topological vector spaces. With the exception of the last section, the scalar field over which vector spaces are defined can be an arbitrary,…
Stieltjes classes for moment-indeterminate probability distributions
  • J. Stoyanov
  • Mathematics
    Journal of Applied Probability
  • 2004
Let F be a probability distribution function with density f. We assume that (a) F has finite moments of any integer positive order and (b) the classical problem of moments for F has a nonunique…
The fixed point for a transformation of Hausdorff moment sequences and iteration of a rational function
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,…
Problème des moments sur les compacts semi-algébriques
Soit K = {x ∈ R n ; p 1 (x) ≥ 0,..., p N (x) ≥ 0} un sous-ensemble semi-algebrique et compact de R n , ou p 1 ,..., p N sont des polynomes normalises par ∥p j ∥∞ , κ ≤ 1 (1 ≤ j ≤ N, N ≥ n + 1), tels…
Solving the truncated moment problem solves the full moment problem
  • J. Stochel
  • Mathematics, Physics
    Glasgow Mathematical Journal
  • 2001
It is shown that the truncated multidimensional moment problem is more general than the full multidimensional moment problem.
...
...