On Markov Moment Problem and Related Results

被引：13

作者：

Olteanu, Octav ^{[1
]}

机构：

[1] Univ Politehn Bucuresti, Dept Math Informat, Splaiul Independentei 313, Bucharest 060042, Romania

来源：

SYMMETRY-BASEL | 2021年 / 13卷 / 06期

关键词：

polynomial approximation; constrained extension of linear operators; Markov moment problem; self-adjoint operator; symmetric matrix; compact subset; spectrum; unbounded subset; basic nonnegative polynomials; truncated moment problem; COMPACT; POLYNOMIALS;

D O I：

10.3390/sym13060986

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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 L nu 1 space, where nu 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.

引用

页数：14

共 38 条

[1]

Ambrozie C., 2004, REV ROUM MATH PURES, V49, P189

[2]

[Anonymous], 2020, The Classical Moment Problem and Some Related Questions in Analysis

[3] Hausdorff means and moment sequences [J].