Absolute Continuity of Complex Martingales and of Solutions to Complex Smoothing Equations

Ewa Damek, Sebastian Mentemeier

Let $X$ be a $\mathbb{C}$-valued random variable with the property that $$X\text{ has the same law as }\sum _{j\ge 1}{T}_j{X}_j$$ where $X_j$ are i.i.d.\ copies of $X$, which are…