On the Moment Problem and Related Problems

  title={On the Moment Problem and Related Problems},
  author={Octav Olteanu},
Firstly, we recall the classical moment problem and some basic results related to it. By its formulation, this is an inverse problem: being given a sequence (yj)j∈ℕn  of real numbers and a closed subset F⊆ℝn, n∈{1,2,…}, find a positive regular Borel measure μ on F such that ∫Ftjdμ=yj, j∈ℕn. This is the full moment problem. The existence, uniqueness, and construction of the unknown solution μ are the focus of attention. The numbers yj, j∈ℕn are called the moments of the measure μ. When a… 


On truncated and full classical Markov moment problems
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 ≤
On Markov Moment Problem and Related Results
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.
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
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
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
Rotation invariant moment problems
An important theorem of Marcel Riesz, cf. [14], states that the polynomials are dense in L2(/x), when/x is a determinate measure on the real line. In the indeterminate case Riesz also characterized
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
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,
On the Momentum Problem for Distribution Functions in More Than One Dimension. II
is likewise non-negative. A. Wintner has subsequently suggested that it should be possible to extend this result by requiring that the distribution function solving the problem have a spectrum