Frames containing a Riesz basis and approximation of the frame coefficients using finite-dimensional methods

Abstract

We consider frames which contain a Riesz basis. Among those, we find Riesz frames, i.e., frames with the property that every subfamily is a frame for its closed linear span, with a common lower bound. We point out the connection to the projection method, which can be used to approximate the frame coefficients for a Riesz frame using finitely many elements of the frame. Under different conditions we show that the projection method even approximates the frame coefficient in l2-sense. © 1996 Academic Press, Inc.