Analytic and asymptotic properties of non-symmetric Linnik's probability densities
The function \[ \varphi_\alpha^\theta(t)= (1+|t|^\alpha \exp(-i\theta \operatorname {sgn} t))^{-1}, \quad \alpha\in (0,2), \;\theta\in (-\pi,\pi], \] is a characteristic function of a probability distribution iff \(|\theta|\leq \min (\pi\alpha/2, \pi- \pi\alpha/2)\). The author carried out a detailed investigation of analytic and asymptotic properties of the density of the distribution for the non-symmetric case \(\theta\neq 0\).
scientific article; zbMATH DE number 1441217