On the orthogonal exponential functions of a class of planar self-affine measures

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:485

Article

Chen, Ming-Liang¹  Wang, Xiang-Yang¹  Zheng, Jia² 

[1] Sun Yat Sen Univ, Sch Math, Guangzhou 510275, Peoples R China

[2] Hunan Normal Univ, Key Lab Comp & Stochast Math, Minist Educ, Sch Math & Stat, Changsha 410081, Hunan, Peoples R China

关键词: Iterated function system;    Self-affine measure;    Orthogonality;    Cardinality;   

DOI  :  10.1016/j.jmaa.2019.123790

来源: Elsevier

【 摘 要 】

For an expanding real matrix M = [(rho-1)(0) (C)(rho-1)] is an element of M2 (R) and a digit setrC-- 1 D = {(0, 0)(t), (1, 0)(t), (0,1)(t), let mu M,D be the self-affine measure generated by M and D. In this paper, we show that L-2(mu(M,D)) admits an infinite orthogonal set of exponential functions if and only if |p| (q/p)(1/r) and C = kappa p(-1) for some positive integers p, q,r with p is an element of 3Z, gcd(p,q) = 1 and a E Q. Moreover, if L-2(mu(M,D)) does not admit any infinite orthogonal set of exponential functions, we estimate the number of orthogonal exponential functions in L2(ktm.D) and give the exact maximal cardinality. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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