Finite shift-invariant subspaces of periodic functions: characterization, approximation, and applications

DOI10.1007/978-3-030-84122-5_5zbMath1496.42031OpenAlexW4300067932MaRDI QIDQ2080458

Nikolaos D. Atreas

Publication date: 7 October 2022

Full work available at URL: https://doi.org/10.1007/978-3-030-84122-5_5

zbMATH Keywords

shift-invariant spacesaverage samplingfinite frames

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) General harmonic expansions, frames (42C15)

Cites Work

• Convolution, average sampling, and a Calderon resolution of the identity for shift-invariant spaces
• Average sampling in shift invariant subspaces with symmetric averaging functions
• Finite normalized tight frames
• Equal-norm tight frames with erasures
• Pairs of oblique duals in spaces of periodic functions
• Generalized sampling in shift-invariant spaces with multiple stable generators
• Riesz bases in \(L^{2}(0,1)\) related to sampling in shift-invariant spaces
• Dual frames in \(L^2(0,1)\) connected with generalized sampling in shift-invariant spaces
• A generalized sampling theory without band-limiting constraints
• Generalized sampling expansion
• Approximation from Shift-Invariant Subspaces of L 2 (ℝ d )
• Frames and Stable Bases for Shift-Invariant Subspaces of L₂(ℝ^d)
• An introduction to frames and Riesz bases
• Quantized frame expansions with erasures

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