An Introduction to Frames and Riesz Bases - Ole Christensen

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Résumé :
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??2(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....

Biographie:
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....

Sommaire:
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 l 2(R).- Gabor Frames in L 2(R).- Gabor Frames and Duality.- Selected Topics on Gabor Frames.- Gabor Frames in??2(Z),L2(0,L),CL.- General Wavelet Frames in 2(R).- Dyadic Wavelet Frames for? 2(R).- Frame Multiresolution Analysis.- Wavelet Frames via Extension Principles.- Selected Topics on Wavelet Frames.- Generalized Shift-Invariant Systems in? 2(Rd).- Frames on Locally Compact Abelian Groups.- Perturbation of Frames.- Approximation of the Inverse Frame Operator.- Expansions in Banach Spaces. Appendix....