Table of Contents

Frames in Finite-dimensional Inner Product Spaces.- Infinite-dimensional Vector Spaces and Sequences.- Bases.- Bases and their Limitations.- Frames in Hilbert Spaces.- Tight Frames and Dual Frame Pairs.- Frames versus Riesz Bases.- Selected Topics in Frame Theory.- Frames of Translates.- Shift-Invariant Systems in l2(R).- Gabor Frames in L2(R).- Gabor Frames and Duality.- Selected Topics on Gabor Frames.- Gabor Frames in ℓ2(Z),L2(0,L),CL.- General Wavelet Frames in L2(R).- Dyadic Wavelet Frames for L2(R).- Frame Multiresolution Analysis.- Wavelet Frames via Extension Principles.- Selected Topics on Wavelet Frames.- Generalized Shift-Invariant Systems in L2(Rd).- Frames on Locally Compact Abelian Groups.- Perturbation of Frames.- Approximation of the Inverse Frame Operator.- Expansions in Banach Spaces. Appendix.

About the Author

Ole Christensen is a Professor at Technical University of Denmark in the Department of Applied Mathematics and Computer Science. His research interests include harmonic analysis, frame expansions, wavelets, and Gabor systems.