Separation via quadratic functions (Q1916963)

The authors consider the problem of separation of two given functions by a quadratic one. They present necessary and sufficient conditions for the quadratic separability in three various cases: when the domain of the functions is an abelian group, a vector space over \(\mathbb{Q}\), and a locally convex topological vector space. Some applications of these results to the representation of second order directional derivatives are also given.