Olteanu, Octav
(2019)
*Polynomial Approximation on Unbounded Subsets
and the Moment Problem.*
In:
Current Research in Science and Technology Vol. 3.
B P International, pp. 137-145.
ISBN http://bp.bookpi.org/index.php/bpi/catalog/book/109

## Abstract

In the first part of this work, one proves a Markov moment problem involving - norm on a space

for a regular positive special measure .. To this end, polynomial approximation on unbounded

subsets and Hahn - Banach principle are applied. One uses approximation by sums of tensor

products of positive polynomials in each separate variable. This way, one solves the difficulty created

by the fact that there are positive polynomials, which are not writable as sums of squares in several

dimensions. Consequently, we can solve the multidimensional moment problem in terms of quadratic

mappings. We also discuss Markov moment problems in concrete spaces. These last results

represent interpolation problems with two constraints. Here the main ingredients of the proofs are

constrained extension theorems for linear operators.

Item Type: | Book Section |
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Subjects: | Eprint Open STM Press > Multidisciplinary |

Depositing User: | Unnamed user with email admin@eprint.openstmpress.com |

Date Deposited: | 02 Dec 2023 05:51 |

Last Modified: | 02 Dec 2023 05:51 |

URI: | http://library.go4manusub.com/id/eprint/1693 |