Frame theory and reproducing kernel Hilbert spaces

In this paper, we discuss various aspects of orthonormal, discrete frame expansions, together with some admissibility conditions with the reproducing kernel Hilbert spaces. We show that all Parseval frames in a Hilbert space are connected by transformations that are unitary between reproducing kernel Hilbert spaces. The purpose of this paper is to present a method for constructing a reproducing kernel Hilbert space and its associated kernel by means of frame theory.