Where do homogeneous polynomials on l1n attain their norm?
نویسندگان
چکیده
Using a ‘reasonable’ measure in P(`1 ), the space of 2homogeneous polynomials on `1 , we show the existence of a set of positive (and independent of n) measure of polynomials which do not attain their norm in the vertices of the unit ball of `1 . Next we prove that, when n grows, the measure of the set of polynomials which attain their norm in a face of ‘high’ dimension of the unit ball tends to 0.
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عنوان ژورنال:
- Journal of Approximation Theory
دوره 127 شماره
صفحات -
تاریخ انتشار 2004