Dual frames in \(L^2(0,1)\) connected with generalized sampling in shift-invariant spaces

DOI10.1016/j.acha.2005.10.001zbMath1090.94012OpenAlexW1971548575MaRDI QIDQ2491729

G. Pérez-Villalón, Antonio G. García

Publication date: 29 May 2006

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.acha.2005.10.001

zbMATH Keywords

dual framesshift-invariant spacesgeneralized sampling

Mathematics Subject Classification ID

General harmonic expansions, frames (42C15) Sampling theory in information and communication theory (94A20)

Related Items (31)

MULTI-CHANNEL SAMPLING ON SHIFT-INVARIANT SPACES WITH FRAME GENERATORS ⋮ Generalized sampling in shift-invariant spaces with multiple stable generators ⋮ Sampling Theory and Reproducing Kernel Hilbert Spaces ⋮ Recovery of missing samples for oversampling in shift invariant spaces ⋮ Generalized sampling in shift invariant spaces with frames ⋮ Reconstruction and error analysis based on multiple sampling functionals over mixed Lebesgue spaces ⋮ A matrix pencil approach to the existence of compactly supported reconstruction functions in average sampling ⋮ GENERALIZED IRREGULAR SAMPLING IN SHIFT-INVARIANT SPACES ⋮ Sampling Formulas Involving Differences in Shift-Invariant Subspaces: A Unified Approach ⋮ Modeling sampling in tensor products of unitary invariant subspaces ⋮ Approximation from shift-invariant spaces by generalized sampling formulas ⋮ A local weighted average sampling and reconstruction theorem over shift invariant subspaces ⋮ Sampling in unitary invariant subspaces associated to LCA groups ⋮ Asymmetric multi-channel sampling in shift invariant spaces ⋮ Regular multivariate sampling and approximation in \(L^p\) shift-invariant spaces ⋮ Using a natural deconvolution for analysis of perturbed integer sampling in shift-invariant spaces ⋮ Knit product of finite groups and sampling ⋮ Aliasing Error of Sampling Series in Wavelet Subspaces ⋮ Oversampling and reconstruction functions with compact support ⋮ Convolution systems on discrete abelian groups as a unifying strategy in sampling theory ⋮ Multivariate generalized sampling in shift-invariant spaces and its approximation properties ⋮ On Regular Generalized Sampling in T-Invariant Subspaces of a Hilbert Space: An Overview ⋮ Average sampling in certain subspaces of Hilbert-Schmidt operators on \(L^2(\mathbb{R}^d)\) ⋮ Sampling in \(\Lambda\)-shift-invariant subspaces of Hilbert-Schmidt operators on \(L^2(\mathbb{R}^d)\) ⋮ Generalized sampling: From shift-invariant to U-invariant spaces ⋮ On some sampling-related frames in \(U\)-invariant spaces ⋮ Average and convolution sampling over shift-invariant spaces ⋮ Finite shift-invariant subspaces of periodic functions: characterization, approximation, and applications ⋮ Sampling associated with a unitary representation of a semi-direct product of groups: a filter bank approach ⋮ Sampling-related frames in finite \(U\)-invariant subspaces ⋮ Average sampling expansions from regular and irregular samples over shift-invariant subspaces on LCA groups

Cites Work

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