Affine Density in Wavelet Analysis
Kutyniok, Gitta.
Affine Density in Wavelet Analysis [electronic resource] / by Gitta Kutyniok. - XII, 143 p. online resource. - Lecture Notes in Mathematics, 1914 0075-8434 ; . - Lecture Notes in Mathematics, 1914 .
Wavelet and Gabor Frames -- Weighted Affine Density -- Qualitative Density Conditions -- Quantitative Density Conditions -- Homogeneous Approximation Property -- Weighted Beurling Density and Shift-Invariant Gabor Systems.
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.
9783540729495
10.1007/978-3-540-72949-5 doi
Fourier analysis.
Mathematics.
Fourier Analysis.
Information and Communication, Circuits.
QA403.5-404.5
515.2433
Affine Density in Wavelet Analysis [electronic resource] / by Gitta Kutyniok. - XII, 143 p. online resource. - Lecture Notes in Mathematics, 1914 0075-8434 ; . - Lecture Notes in Mathematics, 1914 .
Wavelet and Gabor Frames -- Weighted Affine Density -- Qualitative Density Conditions -- Quantitative Density Conditions -- Homogeneous Approximation Property -- Weighted Beurling Density and Shift-Invariant Gabor Systems.
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.
9783540729495
10.1007/978-3-540-72949-5 doi
Fourier analysis.
Mathematics.
Fourier Analysis.
Information and Communication, Circuits.
QA403.5-404.5
515.2433