\(L^q\)-spectrum of Bernoulli convolutions associated with P. V. numbers
Let \(\mu\) be the self-similar measure satisfying the identity \[ \mu = {1 \over 2} \mu \circ \psi_1^{-1} + {1 \over 2} \mu \circ \psi_2^{-1}, \] where \(\psi_1(x) = \rho x, \) \(\psi_2(x) = \rho x + (1-\rho)\), \({1 \over 2} < \rho < 1\). \(\mu\) is called an infinitely convolved Bernoulli measure (ICBM). In this paper, the authors calculate the \(L^q\)-spectrum of \(\mu\) when \(\rho^{-1}\) is a P.V. number and \(q \geq 2\) is an integer.
scientific article; zbMATH DE number 1455447