On truncated and full classical Markov moment problems

@inproceedings{Olteanu2021OnTA,
  title={On truncated and full classical Markov moment problems},
  author={Octav Olteanu},
  year={2021}
}
Abstract Giving necessary and sufficient conditions for the existence of solutions of truncated and full classical Markov moment problems in terms of the given (or measured) moments, in Lp,μ (S) (1 ≤ p <∞) spaces setting, is the first aim of this work. Reduced (truncated) moment problems arise in real-world situations, where only a finite number of samples are available. We obtain solutions as nonnegative functions in a Lq,μ (S) space, where S ⊂ R is a closed subset, μ is a regular Borel… 
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References

SHOWING 1-10 OF 30 REFERENCES
Polynomial Approximation on Unbounded Subsets, Markov Moment Problem and Other Applications
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
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
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
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
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,
Ordered vector spaces and linear operators
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
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.
On the moment problem
The purpose of this paper is to provide some additional insight into the moment problem by connecting a condition by Lin, Bondesson's class of hyperbolically completely monotone densities, and the
From the Hahn–Banach extension theorem to the isotonicity of convex functions and the majorization theory
The property of isotonicity of a continuous convex function on the positive cone is characterized via subdifferentials. This is used to illustrate a new generalization of the Hardy–Littlewood–Polya
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