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Publications Influence

Bounded semigroups of matrices

In this note are proved two conjectures of Daubechies and Lagarias. The first asserts that if Z is a bounded set of matrices such that all left infinite products converge, then 8 generates a bounded… Expand

358 40- PDF

The finiteness conjecture for the generalized spectral radius of a set of matrices

- J. Lagarias, Y. Wang
- Mathematics
- 1995

The generalized spectral radius\g9(∑) of a set ∑ of n × n matrices is \g9(∑) = lim supk→∞\g9k(∑)1k, where \g9k(∑) = sup{ϱ(A1A2…Ak): each Ai ∈ ∑}. The joint spectral radius\g9(∑) is \g9(∑) = lim… Expand

185 23- PDF

Arbitrarily smooth orthogonal nonseparable wavelets in R 2

- E. Belogay, Y. Wang
- Mathematics
- 1 March 1999

For each $r\in\N$, we construct a family of bivariate orthogonal wavelets with compact support that are nonseparable and have vanishing moments of order r or less. The starting point of the… Expand

133 11

Self-affine tiles in ℝn

- J. Lagarias, Y. Wang
- Mathematics
- 15 July 1996

Abstract A self-affine tile in R n is a set T of positive measure with A ( T )=∪ d ∈ D ( T + d ), where A is an expanding n × n real matrix with |det( A )|= m an integer, and D ={ d , d 2 , ..., d… Expand

147 10

Spectral Sets and Factorizations of Finite Abelian Groups

- J. Lagarias, Y. Wang
- Mathematics
- 1 April 1997

Aspectral setis a subsetΩofRnwith Lebesgue measure 0<μ(Ω)<∞ such that there exists a setΛof exponential functions which form an orthogonal basis ofL2(Ω). The spectral set conjecture of B. Fuglede… Expand

88 9- PDF

Integral self-affine tiles in ℝn I. Standard and nonstandard digit sets

- J. Lagarias, Y. Wang
- Mathematics
- 1 August 1996

We investigate the measure and tiling properties of integral self-affine tiles, which are sets of positive Lebesgue measure of the form T(A,@) = { £ * x A~'d^: all d}€@}, where AeMn(Z) is an… Expand

153 7

Orthonormal bases of exponentials for the n-cube

- J. C. Lagarias, J. Reeds, Y. Wang
- Mathematics
- 15 May 2000

Any set that gives such an orthogonal basis is called a spectrum for . Only very special sets in R are spectral sets. However, when a spectrum exists, it can be viewed as a generalization of Fourier… Expand

85 6- PDF

Haar Type Orthonormal Wavelet Bases in R2

- J. Lagarias, Y. Wang
- Mathematics
- 1 February 1995

AbstractK.-H. Grochenig and A. Haas asked whether for every expanding integer matrix
A ∈ Mn(ℤ) there is a Haar type orthonormal wavelet basis having dilation factor A and translation lattice ℤn. They… Expand

50 6

Lattice tiling and the Weyl—Heisenberg frames

- Deguang Han, Y. Wang
- Mathematics
- 1 November 2001

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… Expand

80 6- PDF