The structure of shift-invariant subspaces of Sobolev spaces

DOI10.1134/s0040577924020016MaRDI QIDQ6121935

Aleksandar Aksentijevic, Suzana Aleksić, Stevan Pilipović

Publication date: 26 March 2024

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Sobolev spaceshift-invariant spaceframerange functionBessel family

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Sobolev (and similar kinds of) spaces of functions on metric spaces; analysis on metric spaces (46E36)

Cites Work

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• The structure of translation-invariant spaces on locally compact abelian groups
• Stability of localized operators
• The structure of finitely generated shift-invariant spaces in \(L_ 2(\mathbb{R}^ d)\)
• The spectral function of shift-invariant spaces
• Foundations of time-frequency analysis
• The structure of shift-invariant subspaces of \(L^2(\mathbb{R}^n)\)
• Frames for weighted shift-invariant spaces
• Translation preserving operators on locally compact abelian groups
• Diagonalization of shift-preserving operators
• The structure of finitely generated shift-invariant spaces in mixed Lebesgue spaces \(L^{p,q}\left( {\mathbb{R}}^{d+1}\right)\)
• Dynamical sampling for shift-preserving operators
• Nonuniform Sampling and Reconstruction in Shift-Invariant Spaces
• Approximation from Shift-Invariant Subspaces of L 2 (ℝ d )
• Frames and Stable Bases for Shift-Invariant Subspaces of L₂(ℝ^d)
• \(p\)-frames and shift invariant subspaces of \(L^p\)
• Co-compact Gabor systems on locally compact abelian groups

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