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

@inproceedings{Olteanu2020PolynomialAO,
  title={Polynomial Approximation on Unbounded Subsets, Markov Moment Problem and Other Applications},
  author={Octav Olteanu},
  year={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 natural assumptions, the existence and uniqueness of the solution are deduced. The characterization of the existence of the solution is formulated by two inequalities, one of which involves only quadratic forms. This is the first aim of this work. Characterizing the positivity of a bounded linear… 
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References

SHOWING 1-10 OF 50 REFERENCES
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
Markov Moment Problem in Concrete Spaces Revisited
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
Markov Moment Problem and Related Approximation
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
APPLICATIONS OF HAHN-BANACH PRINCIPLE TO THE MOMENT PROBLEM
. The first aim of this review paper is to show how Hahn-Banach type results can be applied in several aspects related to the multidimensional real moment problem. Here the main tools are constrained
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
An operator-valued moment problem
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
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
SOME NEW ASPECTS OF THE L-MOMENT PROBLEM
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
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