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Asymptotics of signed Bernoulli convolutions scaled by multinacci numbers
| Content Provider | Semantic Scholar |
|---|---|
| Author | Chen, Xianghong Hu, Tian-You |
| Copyright Year | 2017 |
| Abstract | We study the signed Bernoulli convolution $$\nu_\beta^{(n)}=*_{j=1}^n \left (\frac12\delta_{\beta^{-j}}-\frac12\delta_{-\beta^{-j}}\right ),\ n\ge 1$$ where $\beta>1$ satisfies $$\beta^m=\beta^{m-1}+\cdots+\beta+1$$ for some integer $m\ge 2$. When $m$ is odd, we show that the variation $|\nu_\beta^{(n)}|$ coincides the unsigned Bernoulli convolution $$\mu_\beta^{(n)}=*_{j=1}^n \left (\frac12\delta_{\beta^{-j}}+\frac12\delta_{-\beta^{-j}}\right ).$$ When $m$ is even, we obtain the exact asymptotic of the total variation $\|\nu_\beta^{(n)}\|$ as $n\rightarrow\infty$. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://arxiv.org/pdf/1710.01780v1.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
