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- W2085181942 abstract "is the class of plurisubharmonic functions of logarithmic growth (here we have Izl=(L~=1IzjI2)1/2 and log+ Izl=max{O,loglzl}). Then the upper semicontinuous regularization VE(z):=limsuPC-+z VE(() is called the (Siciak) extremal function of E. If K is a compact set in eN, then the extremal function in (1.1) can be gotten via the formula (1.2) VK(Z) :=max{ o,suP{ de~p log Ip(z)l:p holomorphic polynomial, IIpIIK:::; 1} } (Theorem 5.1.7 in [KI]). Here, IlpIlK:=SUPzEKIp(z)1 denotes the uniform norm on K. We say that K is regular if and only if V;=VK. Note that if we let" @default.
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- W2085181942 date "2001-10-01" @default.
- W2085181942 modified "2023-10-01" @default.
- W2085181942 title "On the Siciak extremal function for real compact convex sets" @default.
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