Riesz bases in \(L^{2}(0,1)\) related to sampling in shift-invariant spaces

DOI10.1016/j.jmaa.2004.11.058zbMath1082.94007OpenAlexW2064128003MaRDI QIDQ2484186

G. Pérez-Villalón, Alberto Portal, Antonio G. García

Publication date: 1 August 2005

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.2004.11.058

zbMATH Keywords

Paley-Wiener spacesirregular sampling

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Interpolation in approximation theory (41A05) Sampling theory in information and communication theory (94A20)

Related Items (12)

MULTI-CHANNEL SAMPLING ON SHIFT-INVARIANT SPACES WITH FRAME GENERATORS ⋮ Exact g-frames in Hilbert spaces ⋮ A sampling theorem for the twisted shift-invariant space ⋮ Sampling and reconstruction in shift-invariant spaces on \(\mathbb R^d\) ⋮ GENERALIZED IRREGULAR SAMPLING IN SHIFT-INVARIANT SPACES ⋮ Sampling Formulas Involving Differences in Shift-Invariant Subspaces: A Unified Approach ⋮ Average sampling of band-limited stochastic processes ⋮ Asymmetric multi-channel sampling in shift invariant spaces ⋮ Dual frames in \(L^2(0,1)\) connected with generalized sampling in shift-invariant spaces ⋮ Shift invariant spaces in \(L^2(\mathbb{R},\mathbb{C}^m)\) with \(m\) generators ⋮ Finite shift-invariant subspaces of periodic functions: characterization, approximation, and applications ⋮ Solution of an infinite band matrix equation

Cites Work

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• On the sampling theorem for wavelet subspaces
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• Approximation from Shift-Invariant Subspaces of L 2 (ℝ d )
• Sampling procedures in function spaces and asymptotic equivalence with shannon's sampling theory
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• Frames and Stable Bases for Shift-Invariant Subspaces of L₂(ℝ^d)
• The Zak transform and sampling theorems for wavelet subspaces
• An introduction to frames and Riesz bases
• Frames of translates

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