On Markov Moment Problem and Related Results
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 fun...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/6/986 |
| _version_ | 1797531676648144896 |
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| author | Octav Olteanu |
| author_facet | Octav Olteanu |
| author_sort | Octav Olteanu |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>L</mi><mi>ν</mi><mn>1</mn></msubsup></mrow></semantics></math></inline-formula> space, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula> 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. |
| first_indexed | 2024-03-10T10:48:06Z |
| format | Article |
| id | doaj.art-be243c50e5084dc1976fda9ef02143a1 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T10:48:06Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-be243c50e5084dc1976fda9ef02143a12023-11-21T22:27:43ZengMDPI AGSymmetry2073-89942021-06-0113698610.3390/sym13060986On Markov Moment Problem and Related ResultsOctav Olteanu0Department of Mathematics-Informatics, University Politehnica of Bucharest, Splaiul Independenţei 313, 060042 Bucharest, RomaniaWe 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>L</mi><mi>ν</mi><mn>1</mn></msubsup></mrow></semantics></math></inline-formula> space, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ν</mi></semantics></math></inline-formula> 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.https://www.mdpi.com/2073-8994/13/6/986polynomial approximationconstrained extension of linear operatorsMarkov moment problemself-adjoint operatorsymmetric matrixcompact subset |
| spellingShingle | Octav Olteanu On Markov Moment Problem and Related Results Symmetry polynomial approximation constrained extension of linear operators Markov moment problem self-adjoint operator symmetric matrix compact subset |
| title | On Markov Moment Problem and Related Results |
| title_full | On Markov Moment Problem and Related Results |
| title_fullStr | On Markov Moment Problem and Related Results |
| title_full_unstemmed | On Markov Moment Problem and Related Results |
| title_short | On Markov Moment Problem and Related Results |
| title_sort | on markov moment problem and related results |
| topic | polynomial approximation constrained extension of linear operators Markov moment problem self-adjoint operator symmetric matrix compact subset |
| url | https://www.mdpi.com/2073-8994/13/6/986 |
| work_keys_str_mv | AT octavolteanu onmarkovmomentproblemandrelatedresults |