An Introduction to Frames and Riesz Bases

• Κύριος συγγραφέας: Christensen, Ole (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Cham : Springer International Publishing : Imprint: Birkhäuser, 2016.
• Έκδοση: 2nd ed. 2016.
• Σειρά: Applied and Numerical Harmonic Analysis,
• Θέματα: Mathematics.; Harmonic analysis.; Functional analysis.; Operator theory.; Functional Analysis.; Abstract Harmonic Analysis.; Operator Theory.; Signal, Image and Speech Processing.

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 const...

Πίνακας περιεχομένων:

• 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.