Assume H is a Hilbert space of scalar valued functions on a set X. If for each x?X, the linear functional defined by for each f in the space H is a continuous linear functional then H is called a reproducing kernel Hilbert space (or, simply, a RKHS). Let C(X) denote the set of all the continuous functions on a certain v function f?C(X) denoted by supp(f), is the closure in X of the subset Suppose we have a Hilbert space H all of whose elements are continuous functions on X. We say that disjoint support implies orthogonality in H if for all f,g?H satisfying supp(f)?supp(g)=? there holds =0, where denotes the inner product on H . If disjoint support implies orthogonality in H we also say that H has the orthogonality from disjoint support property. Let H be an RKHS on a topological space X. By the Riesz representation theorem, applied to the continuous linear functional for every x?X, there exists a unique functio K:X× X?C such that K(.,x)? H, for all x?X, and , for all x?X and f?H. (1) The function is called the reproducing kernel for the point x. The two variable function defined by K(y,x)= is called the reproducing kernel for H.