Criteria for hierachical bases in Sobolev spaces

zbMath0957.46026MaRDI QIDQ1969039

Peter Oswald, Rudolph Alexander Lorentz

Publication date: 25 March 2001

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

zbMATH Keywords

Sobolev spaceRiesz basishierarchical systemdual symboldyadic multiresolution analysisexact range of Sobolev exponentsnoncompactly supported functionssmoothness of the dual systemStevenson's hierarchical basis

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15)

Related Items (15)

Riesz multiwavelet bases ⋮ Adaptive wavelet methods on unbounded domains ⋮ Triangular \(\sqrt 3\)-subdivision schemes: The regular case ⋮ Vector cascade algorithms with infinitely supported masks in weighted \(L_2\)-spaces ⋮ Small support spline Riesz wavelets in low dimensions ⋮ Refinable functions with exponential decay: an approach via cascade algorithms ⋮ Criteria for hierachical bases in Sobolev spaces ⋮ Stability analysis of biorthogonal multiwavelets whose duals are not in \(L_2\) and its application to local semiorthogonal lifting ⋮ Characterization of Riesz bases of wavelets generated from multiresolution analysis ⋮ $C^1$ spline wavelets on triangulations ⋮ Smoothness of multivariate refinable functions with infinitely supported masks ⋮ Regularity of refinable functions with exponentially decaying masks ⋮ Dual wavelet frames and Riesz bases in Sobolev spaces ⋮ Multilevel norms for \(H^{-1/2}\) ⋮ Derivative-orthogonal Riesz wavelets in Sobolev spaces with applications to differential equations

Cites Work

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• Experiments in 3D with a three-point hierarchical basis preconditioner
• Simultaneous iteration for computing invariant subspaces of non-Hermitian matrices
• Stable three-point wavelet bases on general meshes
• Regularity of multivariate refinable functions
• Box splines
• The structure of finitely generated shift-invariant spaces in \(L_ 2(\mathbb{R}^ d)\)
• Biorthogonal wavelet expansions
• A robust hierarchical basis preconditioner on general meshes
• Stability of multiscale transformations
• Compactly supported bidimensional wavelet bases with hexagonal symmetry
• Local decomposition of refinable spaces and wavelets
• The lifting scheme: A custom-design construction of biorthogonal wavelets
• A new technique to estimate the regularity of refinable functions
• Criteria for hierachical bases in Sobolev spaces
• Ten Lectures on Wavelets
• Biorthogonal bases of compactly supported wavelets
• Stabilizing the Hierarchical Basis by Approximate Wavelets II: Implementation and Numerical Results
• Characterization of Smoothness of Multivariate Refinable Functions in Sobolev Spaces
• Approximation from Shift-Invariant Subspaces of L 2 (ℝ d )
• Approximation properties of multivariate wavelets
• Construction et Régularité des Fonctions d’Échelle
• Fonctions harmoniques pour un opérateur de transition et applications

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