The square negative correlation property on $$\ell_p^n$$ ℓ p n - balls
| Autor: | David Alonso-Gutiérrez, Julio Bernués |
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| Rok vydání: | 2019 |
| Předmět: |
Unit sphere
General Mathematics 010102 general mathematics Diagonal Orthographic projection Order (ring theory) 0102 computer and information sciences 01 natural sciences Square (algebra) Combinatorics Hyperplane 010201 computation theory & mathematics Orthonormal basis 0101 mathematics Negative correlation Mathematics |
| Zdroj: | Israel Journal of Mathematics. 230:895-917 |
| ISSN: | 1565-8511 0021-2172 |
| DOI: | 10.1007/s11856-019-1840-3 |
| Popis: | In this paper we prove that for any p ∈ [2,∞) the $$\ell_p^n$$ unit ball, $$B_p^n$$ , satisfies the square negative correlation property with respect to every orthonormal basis, while we show it is not always the case for 1 ≤ p ≤ 2. In order to do that we regard $$B_p^n$$ as the orthogonal projection of $$B_p^{n+1}$$ onto the hyperplane $$e_{n+1}^\perp$$ . We will also study the orthogonal projection of $$B_p^n$$ onto the hyperplane orthogonal to the diagonal vector (1, …, 1). In this case, the property holds for all p ≥ 1 and n large enough. |
| Databáze: | OpenAIRE |
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