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Frames, bases, and group representations
Deguang Han,David R. Larson +1 more
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TLDR
In this article, a basic theory for frames and complementary frames and disjointness of unitary systems is presented. But this theory is not applicable to unitary system models.Abstract:
Introduction Basic theory for frames Complementary frames and disjointness Frame vectors for unitary systems Gabor type unitary systems Frame wavelets, super-wavelets and frame sets Frame representations for groups Concluding remarks Bibliography.read more
Citations
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Journal ArticleDOI
Symmetric informationally complete quantum measurements
TL;DR: It is conjecture that a particular kind of group-covariant SIC–POVM exists in arbitrary dimensions, providing numerical results up to dimension 45 to bolster this claim.
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On signal reconstruction without phase
TL;DR: In this paper, the authors construct new classes of Parseval frames for a Hilbert space which allow signal reconstruction from the absolute value of the frame coefficients without using phase or its estimation.
Journal ArticleDOI
Symmetric Informationally Complete Quantum Measurements
TL;DR: In this paper, the authors considered the existence in arbitrary finite dimensions d of a POVM comprised of d^2 rank-one operators all of whose operator inner products are equal, called a ''symmetric, informationally complete'' POVM (SIC-POVM).
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A Douglas–Rachford Splitting Approach to Nonsmooth Convex Variational Signal Recovery
TL;DR: A decomposition method based on the Douglas-Rachford algorithm for monotone operator-splitting for signal recovery problems and applications to non-Gaussian image denoising in a tight frame are demonstrated.
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G-frames and G-Riesz Bases ⁄
TL;DR: G-frames as mentioned in this paper are generalized frames which include ordinary frames, bounded invertible linear operators, as well as many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces.
References
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Journal ArticleDOI
The wavelet transform, time-frequency localization and signal analysis
TL;DR: Two different procedures for effecting a frequency analysis of a time-dependent signal locally in time are studied and the notion of time-frequency localization is made precise, within this framework, by two localization theorems.
Book
Fundamentals of the Theory of Operator Algebras
TL;DR: In this article, the authors compare normal states and unitary equivalence of von Neumann algebras, including the trace and the trace trace of the trace of a projection.
Journal ArticleDOI
Painless nonorthogonal expansions
TL;DR: In a Hilbert space H, discrete families of vectors {hj} with the property that f = ∑j〈hj ǫ à à hj à f à for every f in H are considered.
Book
An introduction to nonharmonic Fourier series
TL;DR: Bases in Banach Spaces - Schauder Bases Schauder's Basis for C[a,b] Orthonormal Bases in Hilbert Space The Reproducing Kernel Complete Sequences The Coefficient Functionals Duality Riesz Bases The Stability of Bases of Complex Exponentials as mentioned in this paper.