Finite-dimensional approximation of the inverse frame operator

DOI10.1007/BF02510119zbMath0961.42020MaRDI QIDQ1976489

Ole Christensen

Publication date: 6 May 2001

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/59632

zbMATH Keywords

frameswavelet frameapproximation of the inverse frame operatorWeil-Heisenberg frame

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Approximation by operators (in particular, by integral operators) (41A35)

Related Items (16)

Optimal adaptive computations in the Jaffard algebra and localized frames ⋮ Finite Fourier frame approximation using the inverse polynomial reconstruction method ⋮ Approximation of the inverse frame operator and stability of Hilbert-Schmidt frames ⋮ Applications of Lax-Milgram theorem to problems in frame theory ⋮ Recovering exponential accuracy from non-harmonic Fourier data through spectral reprojection ⋮ Quasi-orthogonal decompositions of structured frames. ⋮ Detection of edges from nonuniform Fourier data ⋮ Approximation of the inverse frame operator and applications to Gabor frames ⋮ Gabor frames by sampling and periodization ⋮ Approximating the inverse frame operator from localized frames ⋮ Frames of exponentials: Lower frame bounds for finite subfamilies and approximation of the inverse frame operator ⋮ A High-Dimensional Inverse Frame Operator Approximation Technique ⋮ Approximation of dual Gabor frames, window decay, and wireless communications ⋮ Adaptive frame methods for elliptic operator equations ⋮ G-frame operator distance problems ⋮ Frames and Numerical Approximation

Cites Work

• The theory of multiresolution analysis frames and applications to filter banks
• Frames and the projection method
• Frames and pseudo-inverses
• The wavelet transform, time-frequency localization and signal analysis
• Ten Lectures on Wavelets
• Von Neumann algebras and linear independence of translates
• Linear independence of time-frequency translates
• Continuous and Discrete Wavelet Transforms
• Frames of exponentials: Lower frame bounds for finite subfamilies and approximation of the inverse frame operator
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