Where do homogeneous polynomials on ln1 attain their norm?
Using a ‘reasonable’ measure in , the space of 2-homogeneous polynomials on ℓ1n, we show the existence of a set of positive (and independent of n) measure of polynomials which do not attain their norm at the vertices of the unit ball of ℓ1n. Next we prove that, when n grows, almost every polynomial...
| Autores: | , |
|---|---|
| Formato: | artículo |
| Fecha de publicación: | 2004 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/49447 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/49447 |
| Access Level: | acceso abierto |
| Palavra-chave: | 517 Polynomials Extreme points Convex polytopes Vertices Faces Análisis matemático 1202 Análisis y Análisis Funcional |
| Resumo: | Using a ‘reasonable’ measure in , the space of 2-homogeneous polynomials on ℓ1n, we show the existence of a set of positive (and independent of n) measure of polynomials which do not attain their norm at the vertices of the unit ball of ℓ1n. Next we prove that, when n grows, almost every polynomial attains its norm in a face of ‘low’ dimension. |
|---|