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Dynamical sampling
Let Y = {f(i), Af(i), . . . , Ai f(i) : i ∈ Ω}, where A is a bounded operator on `2(I). The problem under consideration is to find necessary and sufficient conditions on A, Ω, {li : i ∈ Ω} in orderExpand
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Accuracy of Lattice Translates of Several Multidimensional Refinable Functions
Complex-valued functionsf1,?,fronRdarerefinableif they are linear combinations of finitely many of the rescaled and translated functionsfi(Ax?k), where the translateskare taken along aExpand
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Wavelets on irregular grids with arbitrary dilation matrices and frame atoms for L2(Rd)
Abstract In this article, we develop a general method for constructing wavelets { | det A j | 1 / 2 ψ ( A j x − x j , k ) : j ∈ J , k ∈ K } on irregular lattices of the form X = { x j , k ∈ R d : j ∈Expand
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Self-similarity and Multiwavelets in Higher Dimensions
Introduction Matrices, tiles, and the joint spectral radius Generalized self-similarity and the refinement equation Multiresolution analysis Examples Bibliography Appendix A. Index of symbols.
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Sums of Cantor sets
We find conditions on the ratios of dissection of a Cantor set so that the group it generates under addition has positive Lebesgue measure. In particular, we answer affirmatively a special case ofExpand
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Furstenberg sets for a fractal set of directions
In this note we study the behavior of the size of Fursten- berg sets with respect to the size of the set of directions dening it. For any pair �;� 2 (0;1), we will say that a set ER 2 is an F��-setExpand
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Iterative actions of normal operators
Let $A$ be a normal operator in a Hilbert space $\mathcal{H}$, and let $\mathcal{G} \subset \mathcal{H}$ be a countable set of vectors. We investigate the relations between $A$, $\mathcal{G}$ , andExpand
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Invariance of a Shift-Invariant Space
A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineeringExpand
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Calculating the Hausdorff Distance Between Curves
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Optimal shift invariant spaces and their Parseval frame generators
Abstract Given a set of functions F = { f 1 , … , f m } ⊂ L 2 ( R d ) , we study the problem of finding the shift-invariant space V with n generators { φ 1 , … , φ n } that is “closest” to theExpand
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