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Frames, bases, and group representations
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 FrameExpand
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Frames for Undergraduates
Introduction Linear algebra review Finite-dimensional operator theory Introduction to finite frames Frames in $\mathbb{R}^2$ The dilation property of frames Dual and orthogonal frames Frame operatorExpand
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FRAMES FOR BANACH SPACES
We use several fundamental results which characterize frames for a Hilbert space to give natural generalizations of Hilbert space frames to general Banach spaces. However, we will see that all ofExpand
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On multiresolution analysis (MRA) wavelets in ℝn
We prove that for any expansive n×n integral matrix A with |det A|=2, there exist A-dilation minimally supported frequency (MSF) wavelets that are associated with a multiresolution analysis (MRA).Expand
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Lattice tiling and the Weyl—Heisenberg frames
Abstract. Let {\cal L} and {\cal K} be two full rank lattices in $ {\Bbb R}^d $. We prove that if $ {\rm v}({\cal L} ) = {\rm v}({\cal K}) $, i.e. they have the same volume, then there exists aExpand
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Frames Associated with Measurable Spaces
TLDR
We present two results dealing with dilation and perturbation properties of general frames, which generalize the works of several authors in the theory of discrete frames. Expand
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Optimal dual frames for erasures
For any given frame (for the purpose of encoding) in a finite dimensional Hilbert space, we investigate its dual frames that are optimal for erasures (for the purpose of decoding). We show that inExpand
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The existence of subspace wavelet sets
Let H be a reducing subspace of L2(Rd), that is, a closed subspace of L2(Rd) with the property that f(Amt - l) ∈ H for any f ∈ H, m ∈ Z and l ∈ Zd, where A is a d × d expansive matrix. It is knownExpand
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FRAME REPRESENTATIONS FOR GROUP-LIKE UNITARY OPERATOR SYSTEMS
Communicated by S Str˘atil˘a Abstract. A group-like unitary system U is a set of unitary operators such that the group generated by the system is contained in TU, where T denotes the unit circle.Expand
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The existence of Gabor bases and frames
For an arbitrary full rank lattice Λ in R and a function g ∈ L(R) the Gabor (or Weyl-Heisenberg) system is G(Λ, g) := {eg(x − κ) ̨ ̨ (κ, `) ∈ Λ}. It is well-known that a necessary condition for G(Λ,Expand
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