Biblioteca de la Universidad Complutense de Madrid

Where do homogeneous polynomials on ln1 attain their norm?

Impacto



Villanueva, Ignacio y Pérez García, David (2004) Where do homogeneous polynomials on ln1 attain their norm? Journal of Approximation Theory, 127 (1). pp. 124-133. ISSN 1096-0430

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URL Oficial: http://www.sciencedirect.com/science/journal/00219045



Resumen

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.


Tipo de documento:Artículo
Palabras clave:Polynomials; Extreme points; Convex polytopes; Vertices; Faces
Materias:Ciencias > Matemáticas > Análisis matemático
Código ID:11658
Depositado:01 Dic 2010 11:08
Última Modificación:08 Feb 2016 15:34

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