Scaling of spectra of self-similar measures with consecutive digits

作者：Wu, Zhi-Yi; Zhu, Meng^*

来源：Journal of Mathematical Analysis and Applications, 2018, 459(1): 307-319.

DOI：10.1016/j.jmaa.2017.10.054

• Self-similar measures
• Orthonormal basis of exponential
• Spectral measures
• Scaling spectra

We consider the equally-weighted Cantor measures Am generated by the iterated function system (IFS) {f(l), (x) = x/p + i/q}(i=0) (q-1), where 2 <= q is an element of Z and q < p is an element of R. It is known that if q divides p, then mu(p,q) is a spectral measure with a spectrum @@@ Lambda p,q = {0, 1, . . . , q - 1} + p{0,1, . . . , q - 1} + p(2) {0, 1, . . . , q - 1} + . . . (finite sum) @@@ (Dai, He and Lai (2013) [6]). In this paper the authors study some positive integers b such that b Lambda(p,q) is also a spectrum of mu(p,q.

• 出版日期2018-3-1
• 单位华中师范大学