. 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 extension theorems for linear functionals or operators. An application using suitable L 1 -polynomial approximation on unbounded subsets is also discussed. One uses approximation by sums of tensor products of positive polynomials in each separate variable. This way, one solves the di ﬃ culty created… Expand

One recalls the relationship between the Markov moment problem and extension of linear functionals (or operators), with two constraints. One states necessary and sufficient conditions for the… Expand

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… Expand

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… Expand

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… Expand

One recalls earlier applications of extension of linear operators with two constraints to the abstract Markov moment problem and Mazur-Orlicz theorem. Next we generalize one of our previous results… Expand

We will remark an extension of a linear functional on subalgebra of algebra of continuous functions on subset of $\mathbb{R}^n$ which preserves positivity.