Bibliographic Details
| Title: |
Orthogonal exponential functions of self-similar measures with consecutive digits in [formula omitted]. |
| Authors: |
Wang, Zhi-Yong1 wzyzzql@163.com, Wang, Zhi-Min1 zmwanghu@163.com, Dong, Xin-Han1 xhdonghnsd@163.com, Zhang, Peng-Fei2 pfzhang@math.cuhk.edu.hk |
| Source: |
Journal of Mathematical Analysis & Applications. Nov2018, Vol. 467 Issue 2, p1148-1152. 5p. |
| Subjects: |
Consecutive interpreting, Orthogonal functions, Exponential functions, Fourier transforms, Mathematical constants |
| Abstract: |
Suppose that 0 < | ρ | < 1 and m ≥ 2 is an integer. Let μ ρ , m be the self-similar measure defined by μ ρ , m ( ⋅ ) = 1 m ∑ j = 0 m − 1 μ ρ , m ( ρ − 1 ( ⋅ ) − j ) . In this paper, we prove that L 2 ( μ ρ , m ) contains an infinite orthonormal set of exponential functions if and only if ρ = ± ( q / p ) 1 / r for some p , q , r ∈ N + with gcd ( p , q ) = 1 and gcd ( p , m ) > 1 . [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
