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

## 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 |
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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: | 08 Feb 2016 15:34 |

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