A note on weighted homogeneous Siciak-Zaharyuta extremal functions

We prove that for any given upper semicontinuous function $φ$ on an open subset $E$ of $\mathbb C^n\setminus\{0\}$, such that the complex cone generated by $E$ minus the origin is connected, the homogeneous Siciak-Zaharyuta function with the weight $φ$ on $E$, can be represented as an envelope of a disc functional.

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