A note on weighted homogeneous Siciak–Zaharyuta extremal functions

We prove that for any given upper semicontinuous function φφ on a subset EE of Cn∖{0}Cn∖{0}, such that the complex cone generated by EE minus the origin is open and connected, the homogeneous Siciak–Zaharyuta function with the weight φφ on EE can be represented as an envelope of a disc functional.