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Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
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Can a locally integrable function be written as the difference of two psh functions?
Let $\varphi$ be a function on a region $\Omega \in C^{n}$ which is locally integrable. Is it true that $\varphi = \psi_{1} -\psi_{2}$ where $\psi_{i}$ are psh?
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Does a (NOT necessarily positive) current have a decomposition formula?
It is well-known that for any positive (1,1)-current $T$, there is a decomposition formula according to [Siu74]. That is, $T$ can be written as an infinite sum of prime divisors plus an extra part. In …