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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 Frame
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 of
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).
Frames Associated with Measurable Spaces
Two results dealing with dilation and perturbation properties of general frames are presented and a necessary and sufficient condition for a representing measure to be an extreme point of the set of representing measures is given.
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 operator
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 a
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.