Published in: Izv. Ross. Akad. Nauk, Ser. Mat., 68 (1998), no. 6,
pp. 27-52.;

English translation: Russian Acad. Sci. Math. Izv., 68 (1998), no. 6.

English translation: Russian Acad. Sci. Math. Izv., 68 (1998), no. 6.

A B S T R A C T

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**

Let
be a Hilbert space of real functions on
the segment with the inner product
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 Here 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.