摘要
Let μM,Dbe a self-affine measure associated with an expanding integer matrix M=[ p1,0,0;p4,p2,0;p5,0,p3]and the digit set D={ 0,e1,e2,e3}in the space R3, where p1,p2,p3∈Z\{ 0,±1 }, p4,p5∈Zand e1,e2,e3are the standard basis of unit column vectors in R3. In this paper, we mainly consider the case p1,p2,p3∈2Z+1, p2≠p3, p4=l(p1−p2), p5=l(p3−p1),where l∈2Z. We prove that μM,Dis a non-spectral measure, and there are at most 4-element μM,D-orthogonal exponentials, and the number 4 is the best. The results here generalize the known results.
Let μM,Dbe a self-affine measure associated with an expanding integer matrix M=[ p1,0,0;p4,p2,0;p5,0,p3]and the digit set D={ 0,e1,e2,e3}in the space R3, where p1,p2,p3∈Z\{ 0,±1 }, p4,p5∈Zand e1,e2,e3are the standard basis of unit column vectors in R3. In this paper, we mainly consider the case p1,p2,p3∈2Z+1, p2≠p3, p4=l(p1−p2), p5=l(p3−p1),where l∈2Z. We prove that μM,Dis a non-spectral measure, and there are at most 4-element μM,D-orthogonal exponentials, and the number 4 is the best. The results here generalize the known results.
作者
Yongli Hu
Zhicheng Zhang
Qi Wang
Yongli Hu;Zhicheng Zhang;Qi Wang(School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xian, China)
