Ball Br Research Articles

Sheltered points in normed spaces

If X is a Hilbert space and V is a subspace, given x e X/V the best approximation IIv(x) to x from V can be constructed in the following way: we consider a ball Br centered at x and intersecting V, then we take the (Chebyshev) center of Br ∩ V. In Banach spaces the centers in V of Br ∩ V (which depend on r) are related to a different map of « approximation ». Here we introduce the notions of « sheltered point » and « shelter » of a bounded set, and we obtain in Banach spaces information about IIv(x) starting from the shelter of Br ∩ V. The notion of sheltered point turns out to be of some interest by itself, since translates problems of simultaneous worst approximation.

On some Hilbert spaces of harmonic functions

Two kinds of spaces of harmonic functions defined on m-dimensional domains are considered. In the first case, the spherical domain is a m-dimensional ball Br in the second case Br is replaced by Br...