Abstract: | We study the class $
\mathfrak{P}_n
$
\mathfrak{P}_n
of algebraic polynomials P
n
(x, y) in two variables of total degree n whose uniform norm on the unit circle Γ1 centered at the origin is at most 1: $
\left\| {P_n } \right\|_{C(\Gamma _1 )}
$
\left\| {P_n } \right\|_{C(\Gamma _1 )}
≤ 1. The extension of polynomials from the class $
\mathfrak{P}_n
$
\mathfrak{P}_n
to the plane with the least uniform norm on the concentric circle Γ
r
of radius r is investigated. It is proved that the values θ
n
(r) of the best extension of the class $
\mathfrak{P}_n
$
\mathfrak{P}_n
satisfy the equalities θ
n
(r) = r
n
for r > 1 and θ
n
(r) = r
n−1 for 0 < r < 1. |