A necessary and sufficient condition for the finite μM,D-orthogonality  

作　　者：LI JianLin 

机构地区：[1]College of Mathematics and Information Science, Shaanxi Normal University

出　　处：《Science China Mathematics》2015年第12期2541-2548,共8页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11171201);the Fundamental Research Fund for the Central University(Grant No.GK201401004)

摘　　要：The self-affine measure μM,D associated with an expanding matrix M ∈ Mn(Z) and a finite digit set D ? Znis uniquely determined by the self-affine identity with equal weight. The set of orthogonal exponential functions E(Λ) := {e2πiλ,x : λ∈Λ} in the Hilbert space L2(μM,D) is simply called μM,D-orthogonal exponentials. We consider in this paper the finiteness of μM,D-orthogonality. A necessary and sufficient condition is obtained for the set E(Λ) to be a finite μM,D-orthogonal exponentials. The research here is closely connected with the non-spectrality of self-affine measures.The self-affine measure μM,D associated with an expanding matrix M ∈ Mn（Z） and a finite digit set D ？ Znis uniquely determined by the self-affine identity with equal weight. The set of orthogonal exponential functions E（Λ） ：= {e2πi λ,x ： λ ∈ Λ} in the Hilbert space L2（μM,D） is simply called μM,D-orthogonal exponentials. We consider in this paper the finiteness of μM,D-orthogonality. A necessary and sufficient condition is obtained for the set E（Λ） to be a finite μM,D-orthogonal exponentials. The research here is closely connected with the non-spectrality of self-affine measures.

关 键 词：iterated function system self-affine measure non-spectrality digit set 

分 类 号：O177.1[理学—数学] P35[理学—基础数学]