Introduction to frames and Riesz bases / Ole Christensen.

Includes bibliographical references and index.

1. Frames in Finite-dimensional Inner Product Spaces.-
2. Infinite-dimensional Vector Spaces and Sequences.-
3. Bases.-
4. Bases and their Limitations.-
5. Frames in Hilbert Spaces.-
6. Tight Frames and Dual Frame Pairs.-
7. Frames versus Riesz Bases.-
8. Selected Topics in Frame Theory.-
9. Frames of Translates.-
10. Shift-Invariant Systems in l2(R).-
11. Gabor Frames in L2(R).-
12. Gabor Frames and Duality.-
13. Selected Topics on Gabor Frames.-
14. Gabor Frames in 2(Z),L2(0,L),CL.-
15. General Wavelet Frames in L2(R).-
16. Dyadic Wavelet Frames for L2(R).-
17. Frame Multiresolution Analysis.-
18. Wavelet Frames via Extension Principles.-
19. Selected Topics on Wavelet Frames.-
20. Generalized Shift-Invariant Systems in L2(Rd).-
21. Frames on Locally Compact Abelian Groups.-
22. Perturbation of Frames.-
23. Approximation of the Inverse Frame Operator.-
24. Expansions in Banach Spaces.
Appendix.

This revised and expanded monograph presents the general theory for frames and Riesz bases in Hilbert spaces as well as its concrete realizations within Gabor analysis, wavelet analysis, and generalized shift-invariant systems. Compared with the first edition, more emphasis is put on explicit constructions with attractive properties. Based on the exiting development of frame theory over the last decade, this second edition now includes new sections on the rapidly growing fields of LCA groups, generalized shift-invariant systems, duality theory for as well Gabor frames as wavelet frames, and open problems in the field.