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Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
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Fourier inversion formula for complex-valued random variables?
The characteristic function of a complex-valued random variable $X$ with pdf $\mu$ is given by
$$
\phi(t) = \int \exp[i \Re(\bar{t} X)] \; d\mu
$$
(or, so says Wikipedia). How does one recover the pd …