Inequalities for convex bodies and polar reciprocal lattices in \(\mathbb{R}^ n\) (Q1346139)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Inequalities for convex bodies and polar reciprocal lattices in \(\mathbb{R}^ n\) |
scientific article; zbMATH DE number 735346
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inequalities for convex bodies and polar reciprocal lattices in \(\mathbb{R}^ n\) |
scientific article; zbMATH DE number 735346 |
Statements
Inequalities for convex bodies and polar reciprocal lattices in \(\mathbb{R}^ n\) (English)
0 references
12 November 1995
0 references
For a lattice \(L\) and an \(o\)-symmetric convex body in \(\mathbb{R}^ n\) let \(\lambda_ i (L, U)\) denote Minkowski's successive minima. Upper bounds are established for \(\lambda_ i (L, U) \lambda_{n-i +1} (L^*, V)\) where \(L^*\) is the dual lattice of \(L\) and \(U\), \(V\) are unit balls of the spaces \(l^ n_ p\), \(1\leq p\leq \infty\). The upper bounds are compared with known lower bounds.
0 references
successive minima
0 references
lattice
0 references
polar body
0 references
