Villanueva Díez, IgnacioPérez García, David2023-06-202023-06-202004-03-01Pérez Garcı́a, D. & Villanueva Díez, I. «Where Do Homogeneous Polynomials on ℓ1n Attain Their Norm?» Journal of Approximation Theory, vol. 127, n.o 1, marzo de 2004, pp. 124-33. DOI.org (Crossref), https://doi.org/10.1016/j.jat.2004.01.001.1096-043010.1016/j.jat.2004.01.001https://hdl.handle.net/20.500.14352/49447Using 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.engjournal articlehttps//doi.org/10.1016/j.jat.2004.01.001http://www.sciencedirect.com/science/journal/00219045open access517PolynomialsExtreme pointsConvex polytopesVerticesFacesAnálisis matemático1202 Análisis y Análisis Funcional