15.2.35 One dimensional random variables and their characteristics

Problem: Let \( \xi \) is a random variable with a symmetrical distribution. Let's substitute \[ \eta=\left\{\begin{array}{l} \xi, \text { when }|\xi| \leq c \\ 0, \text { when }|\xi|>c \end{array}, c>0 .\right. \] Let's denote \( f(t) \) and \( g(t) \) are the characteristic functions of \( \xi \) and \( \eta \) respectively. Prove that there will be such \( \varepsilon>0 \), that \( f(t) \leq g(t) \), when \( |t| \leq \varepsilon \).