Abstract

Let H be a Hilbert space. A set of vectors [Special characters omitted.] ∈ H, i = 1, 2,..., n , x ∈ X , where X is a locally compact space with Borel measure v on it, constitute a rank-n continuous frame, F ([Special characters omitted.] , A, n ) if for each x ∈ X the set [Special characters omitted.] is linearly independent and there exists a positive operator A ∈ GL ( H ) such that [Special characters omitted.] Further the frame becomes discrete if (*) is replaced by [Special characters omitted.] We first study discrete frames and then move to the continuous case, where we develop a connection between frames and reproducing kernels and using this connection we categorize the frames into various kinds. Finally space H using reproducing kernel Hilbert spaces H K on H = L 2 ( X, v, C n ).