Non-Spectrality of Certain Self-Affine Measures on the Generalized Spatial Sierpinski Gasket  

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)

机构地区：[1]School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xian, China

出　　处：《Journal of Applied Mathematics and Physics》2024年第11期3964-3981,共18页应用数学与应用物理（英文）

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.

关 键 词：Sierpinski Gasket Non-Spectrality Orthogonal Exponentials Digit Set 

分 类 号：O17[理学—数学]