On Regular Generalized Sampling in T-Invariant Subspaces of a Hilbert Space: An Overview

DOI10.1080/01630563.2019.1667827zbMath1436.42033arXiv1804.02997OpenAlexW2979385370MaRDI QIDQ5222254

Antonio G. García, G. Pérez-Villalón, María José Muñoz-Bouzo

Publication date: 1 April 2020

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.02997

zbMATH Keywords

dual framesT-invariant subspacesRiesz sequencessampling expansions

Mathematics Subject Classification ID

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

Cites Work

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• Iterative actions of normal operators
• Generalized average sampling in shift invariant spaces
• Sampling in unitary invariant subspaces associated to LCA groups
• Generalized shift-invariant systems and frames for subspaces
• Riesz and frame systems generated by unitary actions of discrete groups
• Multivariate generalized sampling in shift-invariant spaces and its approximation properties
• Average sampling in shift invariant subspaces with symmetric averaging functions
• Sampling theorem for multiwavelet subspaces
• Operator representations of frames: boundedness, duality, and stability
• Oblique dual frames and shift-invariant spaces
• Non-uniform weighted average sampling and reconstruction in shift-invariant and wavelet spaces
• Pseudoframes for subspaces with applications
• Dynamical sampling: time-space trade-off
• Exact reconstruction of signals in evolutionary systems via spatiotemporal trade-off
• Shift-invariant spaces on LCA groups
• Support and approximation properties of Hermite splines
• Convolution systems on discrete abelian groups as a unifying strategy in sampling theory
• Sampling-related frames in finite \(U\)-invariant subspaces
• Generalized sampling in shift-invariant spaces with multiple stable generators
• Dual frames in \(L^2(0,1)\) connected with generalized sampling in shift-invariant spaces
• Existence of Borel transversals in groups
• Dynamical sampling
• Interpolating multiwavelet bases and the sampling theorem
• A generalized sampling theory without band-limiting constraints
• Finite Sampling in Multiple Generated <inline-formula> <tex-math notation="LaTeX">$U$ </tex-math> </inline-formula>-Invariant Subspaces
• Shift-modulation invariant spaces on LCA groups
• A sampling theorem for wavelet subspaces
• A Generalized Sampling Theorem for Locally Compact Abelian Groups
• U-Invariant Sampling: Extrapolation and Causal Interpolation From Generalized Samples
• U-Invariant Sampling and Reconstruction in Atomic Spaces With Multiple Generators
• Generalized sampling: From shift-invariant to U-invariant spaces
• Frame properties of operator orbits
• The Pseudoinverse of an r-Circulant Matrix
• The Pseudoinverse of a Composite Matrix of Circulants
• An introduction to frames and Riesz bases
• Pseudo-duals of frames with applications

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