Separating two classes of samples using support vectors in a convex hull

In this paper, we present the necessary and sufficient conditions of two finite classes of samples that can be separated by a hyperplane in terms of support vectors which are just the vertices of a convex hull of each class of samples. We also extend the calculating formula of the margin of an optimal separating hyperplane to some cases of the classes of infinite samples in Hilbert space. These results are the generalization and improvement of the corresponding results for the theory of SVM in Euclidian space.