Villanueva, Ignacio and Pérez García , David (2004) Where do homogeneous polynomials on ln1 attain their norm? Journal of Approximation Theory, 127 (1). pp. 124133. ISSN 10960430

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Official URL: http://www.sciencedirect.com/science/journal/00219045
Abstract
Using a ‘reasonable’ measure in , the space of 2homogeneous 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.
Item Type:  Article 

Uncontrolled Keywords:  Polynomials; Extreme points; Convex polytopes; Vertices; Faces 
Subjects:  Sciences > Mathematics > Mathematical analysis 
ID Code:  11658 
Deposited On:  01 Dec 2010 11:08 
Last Modified:  06 Feb 2014 09:08 
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