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- Publications
- Influence
Dynamical sampling
- A. Aldroubi, C. Cabrelli, U. Molter, S. Tang
- Mathematics
- 29 September 2014
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 order… Expand
Accuracy of Lattice Translates of Several Multidimensional Refinable Functions
- C. Cabrelli, C. Heil, U. Molter
- Mathematics
- 1 October 1998
Complex-valued functionsf1,?,fronRdarerefinableif they are linear combinations of finitely many of the rescaled and translated functionsfi(Ax?k), where the translateskare taken along a… Expand
Wavelets on irregular grids with arbitrary dilation matrices and frame atoms for L2(Rd)
- A. Aldroubi, C. Cabrelli, U. Molter
- Mathematics
- 1 September 2004
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
Self-similarity and Multiwavelets in Higher Dimensions
- C. Cabrelli, C. Heil, U. Molter
- Mathematics
- 1 July 2004
Introduction Matrices, tiles, and the joint spectral radius Generalized self-similarity and the refinement equation Multiresolution analysis Examples Bibliography Appendix A. Index of symbols.
Sums of Cantor sets
- C. Cabrelli, Kathryn E. Hare, U. Molter
- Mathematics
- 1 December 1997
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 of… Expand
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��-set… Expand
Iterative actions of normal operators
- A. Aldroubi, C. Cabrelli, A. cCakmak, U. Molter, A. Petrosyan
- Mathematics
- 14 February 2016
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 $A$, $\mathcal{G}$ , and… Expand
Invariance of a Shift-Invariant Space
- A. Aldroubi, C. Cabrelli, C. Heil, K. Kornelson, U. Molter
- Mathematics
- 10 April 2008
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 engineering… Expand
Calculating the Hausdorff Distance Between Curves
- E. Belogay, C. Cabrelli, U. Molter, R. Shonkwiler
- Mathematics, Computer Science
- Inf. Process. Lett.
- 14 October 1997
Optimal shift invariant spaces and their Parseval frame generators
- A. Aldroubi, Carlos Cabrelli, D. Hardin, U. Molter
- Mathematics
- 1 September 2007
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 the… Expand