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Where do homogeneous polynomials on ln1 attain their norm?

Villanueva, Ignacio and 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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Abstract

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.


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:04 Dec 2014 11:46

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