Operator-valued frames

DOI10.1090/S0002-9947-09-04915-0zbMath1185.42032arXiv0707.3272MaRDI QIDQ3648197

David R. Larson, Victor Kaftal, Shuang Zhang

Publication date: 24 November 2009

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.3272

zbMATH Keywords

group representationsframeshomotopymultiframes

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Several-variable operator theory (spectral, Fredholm, etc.) (47A13) General theory of (C^*)-algebras (46L05) General harmonic expansions, frames (42C15)

Related Items (32)

Some identities and inequalities for Hilbert-Schmidt frames ⋮ Wandering operators for unitary systems of Hilbert spaces ⋮ \(K\)-fusion frames and the corresponding generators for unitary systems ⋮ Frames and factorization of graph Laplacians ⋮ Gabor duals for operator-valued Gabor frames on locally compact abelian groups ⋮ Weaving frames in Hilbert \(C^\ast\)-modules ⋮ Approximation of the inverse frame operator and stability of Hilbert-Schmidt frames ⋮ On the Riesz fusion bases in Hilbert spaces ⋮ Wavelet frames in \(L^2(\mathbb{R}^{d})\) ⋮ Decomposition of Gaussian processes, and factorization of positive definite kernels ⋮ Dilations of dual \(g\)-frame generators for an abstract wavelet system ⋮ Bridging erasures and the infrastructure of frames ⋮ Fusion frame homotopy and tightening fusion frames by gradient descent ⋮ Operator valued frames and structured quantum channels ⋮ The effect of perturbations of frames and fusion frames on their redundancies ⋮ Operator-valued frames for the Heisenberg group ⋮ Dilations of operator-valued measures with bounded \(p\)-variations and framings on Banach spaces ⋮ Unnamed Item ⋮ Duality in reconstruction systems ⋮ Manufacturing pairs of woven frames applying duality principle on Hilbert spaces ⋮ Positive operator-valued measures and densely defined operator-valued frames ⋮ The Banach spaces associated with g-frames ⋮ Weaving \(g\)-frames and weaving fusion frames ⋮ Decomposition of Analysis Operators and Frame Ranges for Continuous Frames ⋮ Operator-Valued Measures, Dilations, and the Theory of Frames ⋮ Signal reconstruction from frame and sampling erasures ⋮ Factorable weak operator-valued frames ⋮ Characterizing the R-duality of g-frames ⋮ Characterizations of the dilation of frame generator dual pairs for group ⋮ Unnamed Item ⋮ Infinite networks and variation of conductance functions in discrete Laplacians ⋮ Expansion of weak reconstruction sequences to approximate Schauder frames for Banach spaces

Cites Work

• Optimal linear transmission by loss-insensitive packet encoding
• Fusion frames and distributed processing
• Ellipsoidal tight frames and projection decompositions of operators
• Frames, graphs and erasures
• On signal reconstruction without phase
• \(g\)-frames and \(g\)-Riesz bases
• The Kadison–Singer Problem in mathematics and engineering
• Operator valued frames on C*-modules
• Wandering vectors for unitary systems and orthogonal wavelets
• Frames, bases and group representations
• The Pythagorean Theorem: II. The infinite discrete case
• Wavelets, Frames and Operator Theory
• Remarks on Naimark’s duality
• An introduction to frames and Riesz bases
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