On the orthogonality of frames and the density and connectivity of wavelet frames

DOI10.1007/s10440-008-9420-2zbMath1175.42013OpenAlexW2031861120MaRDI QIDQ1038747

David R. Larson, De Guang Han

Publication date: 20 November 2009

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10440-008-9420-2

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Linear operators belonging to operator ideals (nuclear, (p)-summing, in the Schatten-von Neumann classes, etc.) (47B10) General harmonic expansions, frames (42C15)

Related Items (11)

Nilpotent bridging for unions of two bases ⋮ Unitary Systems and Bessel Generator Multipliers ⋮ Pairwise orthogonal frames generated by regular representations of LCA groups ⋮ Orthogonality of a pair of frames over locally compact abelian groups ⋮ On the direct path problem of \(s\)-elementary frame wavelets ⋮ Path-connectedness and topological closure of some sets related to the non-compact Stiefel manifold ⋮ Characterization of matrix Fourier multiwavelet frames multipliers with integer dilation factor ⋮ Density of frame wavelets and tight frame wavelets in local fields ⋮ Frame vector multipliers for finite group representations ⋮ Matrix Fourier multipliers for Parseval multi-wavelet frames ⋮ The density theorem of a class of dilation-and-modulation systems on the half real line

Cites Work

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• Topological and geometric properties of refinable functions and MRA affine frames
• Smoothing minimally supported frequency wavelets. II
• Basic properties of wavelets
• Connectivity, homotopy degree, and other properties of \(\alpha\)-localized wavelets on \(\mathbb{R}\)
• Smoothing minimally supported frequency wavelets. I
• Frame wavelets with frame set support in the frequency domain
• Orthogonal frames of translates
• Tight frame wavelets, their dimension functions, MRA tight frame wavelets and connectivity properties
• The uniqueness of the dual of Weyl--Heisenberg subspace frames
• Connectivity and density in the set of framelets
• MRA super-wavelets
• Density of the set of generators of wavelet systems
• A pair of orthogonal frames
• Wandering vector multipliers for unitary groups
• Encryption Schemes using Finite Frames and Hadamard Arrays
• Further results on the connectivity of Parseval frame wavelets
• Oversampling generates super-wavelets
• Frame representations and Parseval duals with applications to Gabor frames
• Wandering vectors for unitary systems and orthogonal wavelets
• The s-elementary wavelets are path-connected
• Connectivity in the set of Tight Frame Wavelets (TFW)
• Frames, bases and group representations
• Frame wavelets in subspaces of $L^2(\mathbb R^d)$
• Approximations for Gabor and wavelet frames
• Geometric aspects of frame representations of abelian groups
• The s-elementary frame wavelets are path connected
• POSITIVE DEFINITE MAPS, REPRESENTATIONS AND FRAMES
• Completeness in the set of wavelets

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