st.statistics - Uniqueness of the function used in the Khinchine criterion for characteristic function

Wednesday, 2 March 2011

st.statistics - Uniqueness of the function used in the Khinchine criterion for characteristic function

Khinchine criterion for $varphi$ being a characteristic functions states that it is a ch.f. if and only if $varphi(0)=1$ and

$varphi(t) = int_{-infty}^infty g(t+theta) overline{g(theta)} dtheta$

Is function $g$ uniquely defined for a given $varphi$ ?

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