Approximation and Markov moment problem on concrete spaces

2021

Symmetry

Self Cite

We prove new results and complete our recently published theorems on the vector-valued Markov moment problem, by means of polynomial approximation on unbounded subsets, also applying an extension of the positive linear operators’ result. The domain is the Banach lattice of continuous real-valued functions on a compact subset or an space, where is a positive moment determinate measure on a closed unbounded set. The existence and uniqueness of the operator solution are proved. Our solutions satisfy the interpolation moment conditions and are between two given linear operators on the positive cone of the domain space. The norm controlling of the solution is emphasized. The most part of the results are stated and proved in terms of quadratic forms. This type of result represents the first aim of the paper. Secondly, we construct a polynomial solution for a truncated multidimensional moment problem.

Section: Polynomial Approximation On Unbounded Subsetsmentioning

confidence: 99%

On Markov Moment Problem and Related Results

2021

Symmetry

Self Cite

“…Theorem-4.1. (see [16]) Let n R A  be a closed unbounded subset and  a positive regular  M determinate Borel measure [7] on , A with finite moments of all orders. Then for any…”

Section: Polynomial Approximation On Unbounded Subsets and The Multidimensional Moment Problemmentioning

confidence: 99%

“…For basic notions of the present work, we mention the monographs [2][3][4][5][6], [7]. For applications of polynomial decomposition and approximation to the moment problem see [2], [8][9][10][11][12][13], [14][15][16][17]. An approximation method similar to ours, applied to the complex moment problem, appears in [9].…”

Section: Introductionmentioning

confidence: 99%

Applied Optimization and Approximation

2014

Self Cite

The present work deals with optimization in kinematics, generalizing previous results of the author. A second theme is maximizing the constrained gain linear function and minimizing the constrained cost function. Elementary notions of optimal control are considered as well. Finally, polynomial approximation results on unbounded subsets in several variables are applied to the moment problem. The existence of the solution of a two dimensional moment problem is characterized in terms of quadratic forms.

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

2020

Mathematics

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 operator only by means of quadratic forms is the second aim. From the latter point of view, one solves completely the difficulty arising from the fact that there exist nonnegative polynomials on ℝn, n≥2, which are not sums of squares.