Augustin, Doris (2012) The Membership Problem for finitely generated quadratic modules in the univariate case. JOURNAL OF PURE AND APPLIED ALGEBRA, 216 (10). pp. 2204-2212. ISSN 0022-4049,
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We prove that the Membership Problem is solvable affirmatively for every finitely generated quadratic module Q of R[X-1]. For the case that the associated semialgebraic set S is bounded we show that a polynomial f is an element of Q if and only if f is nonnegative on S and fulfills certain order conditions in the boundary points of S. This leads us to the definition of generalized natural generators of the quadratic module Q. (C) 2012 Elsevier B.V. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | MULTIDIMENSIONAL MOMENT PROBLEM; POLYNOMIALS; SQUARES; SUMS; REPRESENTATIONS; POSITIVITY; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 06 May 2020 05:13 |
| Last Modified: | 06 May 2020 05:13 |
| URI: | https://pred.uni-regensburg.de/id/eprint/18089 |
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