• DOI:10.47443/cm.2021.0011
• Corpus ID: 233031955

On truncated and full classical Markov moment problems

@inproceedings{Olteanu2021OnTA,
  title={On truncated and full classical Markov moment problems},
  author={Octav Olteanu},
  year={2021}
}

• Octav Olteanu
• Published 2021
• Mathematics

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 probability measure on S and q is the conjugate of p ∈ [1,∞) . Applying polynomial approximation on Cartesian products of closed unbounded intervals in solving full Markov moment problems on [0,∞), when the uniqueness of the solution follows too, is the second purpose of the paper. A construction of a solution for the truncated one-dimensional moment problem is proposed. Influence of perturbations of the moments on the corresponding solutions in L2,μ (S) is also briefly discussed; this is the third aim of the paper.