5 papers · 1 filter
Perturbations of Weyl-Heisenberg frames
Peter G. Casazza, Ole Christensen, Mark C. Lammers
We develop a usable perturbation theory for Weyl-Heisenberg frames. In particular, we prove that if $(E_{mb}T_{na}g)_{m,n\inmathbb Z}$ is a WH-frame and is a function which is…
Weyl-Heisenberg Frames, Translation Invariant Systems and the Walnut Representation
Peter G. Casazza, Ole Christensen, A. J. E. M. Janssen
We present a comprehensive analysis of the convergence properties of the frame operators of Weyl-Heisenberg systems and shift-invariant systems, and relate these to the convergence…
Classifying Tight Weyl-Heisenberg Frames
Peter G. Casazza, Ole Christensen
A Weyl-Heisenberg frame for L^2(R) is a frame consisting of translates and modulates of a fixed function. In this paper we give necessary and sufficient conditions for this family…
Weyl-Heisenberg frames for subspaces of L^2(R)
Peter G. Casazza, Ole Christensen
We give sufficient conditions for translates and modulates of a function g in L^2(R) to be a frame for its closed linear span. Even in the case where this family spans all of L^2(R…
Frames of translates
Peter G. Casazza, Ole Christensen, Nigel J. Kalton
We give necessary and sufficient conditions for a subfamily of regularly spaced translates of a function to form a frame (resp. a Riesz basis) for its span. One consequence is that…