# necessary and sufficient conditions for a function to be DC

Hi, Does anyone know the necessary and sufficient conditions for a function to be a DC-function?

Definition: A function is a DC-function if and only if it can be written as a differnece of 2 convex functions.

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$x \: \mapsto \: x^4-0 \;\;$ seems like a counterexample to the necessity. $\;\;\;\;$ – Ricky Demer Nov 15 '12 at 7:47