Abstract
We show that the problem of finding the measure supported on a compact set $$K\subset \mathbb {C}$$
K
⊂
C
such that the variance of the least squares predictor by polynomials of degree at most n at a point $$z_0\in \mathbb {C}^d\backslash K$$
z
0
∈
C
d
\
K
is a minimum is equivalent to the problem of finding the polynomial of degree at most n, bounded by 1 on K, with extremal growth at $$z_0.$$
z
0
.
We use this to find the polynomials of extremal growth for $$[-1,1]\subset \mathbb {C}$$
[
-
1
,
1
]
⊂
C
at a purely imaginary point. The related problem on the extremal growth of real polynomials was studied by Erdős (Bull Am Math Soc 53:1169–1176, 1947).