Haar-type multiwavelet bases and self-affine multi-tiles
نویسندگان
چکیده
منابع مشابه
Haar - Type Multiwavelet Bases and Self - Affine Multi - Tiles
Abstract. Gröchenig and Madych showed that a Haar-type wavelet basis of L2(Rn) can be constructed from the characteristic function χΩ of a compact set Ω if and only if Ω is an integral self-affine tile of Lebesgue measure one. In this paper we generalize their result to the multiwavelet settings. We give a complete characterization of Haar-type scaling function vectors χΩ(x) := [χΩ1 (x), . . . ...
متن کاملHAAR - TYPE MULTIWAVELET BASES AND SELF - AFFINE MULTI - TILES 389 Theorem 1
Grr ochenig and Madych showed that a Haar-type wavelet basis of L 2 (R n) can be constructed from the characteristic function of a compact set if and only if is an integral self-aane tile of Lebesgue measure one. In this paper we generalize their result to the multiwavelet settings. We give a complete characterization of Haar-type scaling function vectors (x) := 1 (x); : : : ; r (x)] T , where ...
متن کاملRational Self-affine Tiles
An integral self-affine tile is the solution of a set equation AT = ⋃d∈D(T +d), where A is an n× n integer matrix and D is a finite subset of Z. In the recent decades, these objects and the induced tilings have been studied systematically. We extend this theory to matrices A ∈ Qn×n. We define rational self-affine tiles as compact subsets of the open subring R ×∏pKp of the adèle ring AK , where ...
متن کاملSelf-Affine Tiles in Rn
A self-affine tile in R is a set T of positive measure with A(T) = d ∈ $ < (T + d), where A is an expanding n × n real matrix with det (A) = m on integer, and $ = {d 1 ,d 2 , . . . , d m } ⊆ R is a set of m digits. It is known that self-affine tiles always give tilings of R by translation. This paper extends the known characterization of digit sets $ yielding self-affine tiles. It proves seve...
متن کاملGeometry of Self { Affine Tiles
For a self{similar or self{aane tile in R n we study the following questions: 1) What is the boundary? 2) What is the convex hull? We show that the boundary is a graph directed self{aane fractal, and in the self{similar case we give an algorithm to compute its dimension. We give necessary and suucient conditions for the convex hull to be a polytope, and we give a description of the Gauss map of...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Asian Journal of Mathematics
سال: 1999
ISSN: 1093-6106,1945-0036
DOI: 10.4310/ajm.1999.v3.n2.a7