INTEGRAL SELF-AFFINE TILES IN R-N .2. LATTICE TILINGS

Authors
LAGARIAS JC WANG Y
Citation
Jc. Lagarias et Y. Wang, INTEGRAL SELF-AFFINE TILES IN R-N .2. LATTICE TILINGS, The journal of fourier analysis and applications, 3(1), 1997, pp. 83-102
Citations number
30
Categorie Soggetti
Mathematics,Mathematics
Journal title
The journal of fourier analysis and applications → ACNP
ISSN journal
10695869
Volume
3
Issue
1
Year of publication
1997
Pages
83 - 102
Database
ISI
SICI code
1069-5869(1997)3:1<83:ISTIR.>2.0.ZU;2-4
Abstract
Let A be an expanding n x n integer matrix with \det(A)\ = m. A standa rd digit set D for A is any complete set of coset representatives for Z(n)/A(Z(n)). Associated to a given 2) is a set T(A, D), which is the attractor of an affine iterated function system, satisfying T = U (d i s an element of D) (T + d) It is known that T(A, D) tiles R-n by some subset of Z(n). This paper proves that every standard digit set D give s a set T(A, D) that tiles R-n with a lattice tiling.