Asymptotics of signed Bernoulli convolutions scaled by multinacci numbers

Xianghong Chen, Tian-You Hu

We study the signed Bernoulli convolution $${\nu }_{\beta }^{(n)}={\ast }_{j=1}^n\left(\frac{1}{2}{\delta }_{{\beta }^{-j}}-\frac{1}{2}{\delta }_{-{\beta }^{-j}}\right),n\ge 1$$ where $\beta >1$ satisfies $${\beta }^m={\beta }^{m-1}+\cdots +\beta +1$$ for…