TY  - BOOK
AU  - Kutyniok,Gitta
ED  - SpringerLink (Online service)
TI  - Affine Density in Wavelet Analysis
T2  - Lecture Notes in Mathematics,
SN  - 9783540729495
AV  - QA403.5-404.5 
U1  - 515.2433 23
PY  - 2007///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Fourier analysis
KW  - Fourier Analysis
KW  - Information and Communication, Circuits
N1  - Wavelet and Gabor Frames -- Weighted Affine Density -- Qualitative Density Conditions -- Quantitative Density Conditions -- Homogeneous Approximation Property -- Weighted Beurling Density and Shift-Invariant Gabor Systems
N2  - In wavelet analysis, irregular wavelet frames have recently come to the forefront of current research due to questions concerning the robustness and stability of wavelet algorithms. A major difficulty in the study of these systems is the highly sensitive interplay between geometric properties of a sequence of time-scale indices and frame properties of the associated wavelet systems. This volume provides the first thorough and comprehensive treatment of irregular wavelet frames by introducing and employing a new notion of affine density as a highly effective tool for examining the geometry of sequences of time-scale indices. Many of the results are new and published for the first time. Topics include: qualitative and quantitative density conditions for existence of irregular wavelet frames, non-existence of irregular co-affine frames, the Nyquist phenomenon for wavelet systems, and approximation properties of irregular wavelet frames
UR  - http://dx.doi.org/10.1007/978-3-540-72949-5
ER  -