Analysis of a class of spectral pair conditions

作     者：LI JianLin 

作者机构：College of Mathematics and Information Science Shaanxi Normal University Xi'an 710062 China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2011年第54卷第10期

页      面：2099-2110页

核心收录：

学科分类：07[理学] 08[工学] 070104[理学-应用数学] 0805[工学-材料科学与工程（可授工学、理学学位）] 080502[工学-材料学] 0701[理学-数学] 

基　　金：supported by the Key Project of Chinese Ministry of Education (Grant No. 108117) National Natural Science Foundation of China (Grant No. 10871123, 11171201) 

主　　题：iterated function system self-affine measure spectral pair compatible pair digit set 

摘      要：For an expanding integer matrix M ∈ Mn（Z） and two finite digit sets D, S C Z^n with O∈ D ∩ S, we shall investigate and study the possible conditions on the spectral pair （μM,D,A（M, S）） associated with the iterated function systems {Фd（X） = M^-1（x ＋ d）}d∈D and {φs（x） = M^＊x ＋ s}s∈S in the case when ｜D｜= ｜S｜ = ｜ det（M）｜. Under the condition that （M^-1D, S） is a compatible pair, we obtain a series of necessary and sufficient conditions for （μM,D, A（M, S）） to be a spectral pair. These conditions include how to characterize the invariant sets A（M, S） and T（M, D） such that A（M, S） = Zn and μL（T（M, D）） = 1 which play an important role in the number system research and in the construction of Haar-type orthogonal wavelet basis respectively.