An effective strategy for accelerating the calculation of convex hulls for point sets is to filter the input points by discarding interior points. In this paper, we present such a straightforward and efficient preprocessing approach by exploiting the GPU. The basic idea behind our approach is to discard the points that locate inside a convex polygon formed by 16 extreme points. Due to the fact ...

We prove that all extreme points of the unit ball a Lipschitz-free space over compact metric have finite support. Combined with previous results, this completely characterizes and implies them are also in bidual ball. For proof, we develop some properties an integral representation functionals on Lipschitz spaces originally due to K. de Leeuw.

The Hardy space $H^1$ consists of the integrable functions $f$ on unit circle whose Fourier coefficients $\widehat f(k)$ vanish for $k<0$. We are concerned with that have some additional (finitely many) holes in spectrum, so we fix a finite set $\mathcal K$ positive integers and consider "punctured" $$H^1_{\mathcal K}:=\{f\in H^1:\,\widehat f(k)=0\,\,\,\text{for all }\, k\in\mathcal K\}.$$ then...