The work was published in:
Mat. Zametki 60 (1996), no. 3, pp. 333-355;
English translation: Math. Notes. 60 (1996), no. 3, pp. 248-263.
S U M M A R Y
41A17 41A44
B a b e n k o A. G.
Exact Jackson-Stechkin type inequality in
space of functions
on the multidimensional sphere.
In this paper we prove Jackson-Stechkin type inequality
which is exact for every
here
is the best approximation of the function
by
spherical polynomials of degree
is the
th modulus of continuity of
based on translation
is the measure of the unit Euclidean sphere
is the first positive zero
of the Gegenbauer's cosine polynomial
.