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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

57 8- PDF

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

98 7- PDF

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

101 6- PDF

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.

79 5

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

29 4

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

23 3- PDF

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

49 3- PDF

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

36 3- PDF

Calculating the Hausdorff Distance Between Curves

- E. Belogay, C. Cabrelli, U. Molter, R. Shonkwiler
- Mathematics, Computer Science
- Inf. Process. Lett.
- 14 October 1997

88 2

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

34 2- PDF