Generalized sampling in shift-invariant spaces with multiple stable generators

DOI10.1016/j.jmaa.2007.03.083zbMath1133.42048OpenAlexW2088337169MaRDI QIDQ2382686

G. Pérez-Villalón, Miguel Ángel Hernández-Medina, Antonio G. García

Publication date: 2 October 2007

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.03.083

zbMATH Keywords

frames

Mathematics Subject Classification ID

General harmonic expansions, frames (42C15) Completeness of sets of functions in nontrigonometric harmonic analysis (42C30) Sampling theory in information and communication theory (94A20)

Related Items (21)

MULTI-CHANNEL SAMPLING ON SHIFT-INVARIANT SPACES WITH FRAME GENERATORS ⋮ Approximation of kernel projection operators in shift-invariant subspaces of function spaces with mixed norms ⋮ Generalized sampling in shift invariant spaces with frames ⋮ A matrix pencil approach to the existence of compactly supported reconstruction functions in average sampling ⋮ Invertibility of Laurent operators and shift invariant spaces with finitely many generators ⋮ Sampling and Reconstruction in a Shift Invariant Space with Multiple Generators ⋮ Quantum tomography and the quantum Radon transform ⋮ Modeling sampling in tensor products of unitary invariant subspaces ⋮ A local weighted average sampling and reconstruction theorem over shift invariant subspaces ⋮ Local Sampling and Reconstruction in Shift-Invariant Spaces and Their Applications in Spline Subspaces ⋮ Regular multivariate sampling and approximation in \(L^p\) shift-invariant spaces ⋮ Constructive realization of dual systems for generators of multi-window spline-type spaces ⋮ Shortest-support multi-spline bases for generalized sampling ⋮ Reconstruction of Multiply Generated Splines from Local Average Samples ⋮ 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 ⋮ Average and convolution sampling over shift-invariant spaces ⋮ Finite shift-invariant subspaces of periodic functions: characterization, approximation, and applications ⋮ Average sampling expansions from regular and irregular samples over shift-invariant subspaces on LCA groups

Cites Work

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• Oblique projections in atomic spaces
• An introduction to frames and Riesz bases

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