On the exact constant in Jackson-Stechkin inequality for the uniform metric

Details On the exact constant in Jackson-Stechkin inequality for the uniform metric On the exact constant in Jackson-Stechkin inequality for the uniform metric

2006-12-11

arxiv.org/abs/math/0612283v1

Mathematics

Classical Analysis and ODEs

20 pages

Scientific paper

The classical Jackson-Stechkin inequality estimates the value of the best uniform approximation of a periodic function by trigonometric polynomials of degree $\le n-1$ in terms of its $r$-th modulus of smoothness $\omega_r(f,\delta)$. The main result of the paper is in establishing the correct order of Jackson--Stechkin constants.

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