Approximation of the inverse frame operator and applications to Gabor frames

A frame allows every element in a Hilbert space H to be written as a Linear combination of the frame elements, with coefficients called frame coeffici ents. Calculation of the frame coeffrcients requires inversion of an operat or S on H. We show how the inverse of S can be approximated as close as we like using finite-dimensional linear algebra. In contrast with previous met hods, our approximation can be used for any frame. Various consequences for approximation of the frame coefficients or approximation of the solution t o a moment problem are discussed. We also apply the results to Gabor frames and frames consisting of translates of a single function. (C) 2000 Academi c Press.