Published in: Izv. Ross. Akad. Nauk, Ser. Mat., 68 (1998), no. 6,
English translation: Russian Acad. Sci. Math. Izv., 68 (1998), no. 6.
A B S T R A C T
be a Hilbert space of real functions on
the segment with the inner product
B a b e n k o A. G.
Exact Jackson - Stechkin Inequality for
- Approximations on the Segment with Jacobi Weight
and on Projective Spaces
In the paper had been proved that
exact Jackson - Stechkin inequality
among the best approximation of the function by cosine
polynomials of the order and its generalized modulus of
continuity of the (real) order is valid
in the case
is the first positive zero of Jacobi cosine polynomial
Analogouse results for mean squared approximations of functions
of many variables given on the projective spaces
are deduced from here.
Bibliogr. 49 titles.