Jackson-Stechkin-type inequalities for the approximation of elements of Hilbert spaces (Q2319565)

The authors introduce moduli of continuity for elements of Hilbert spaces and obtain some new exact Jackson-Stechkin-type inequalities for the approximation of elements of Hilbert spaces. These inequalities contain several well-known inequalities for the best \(L_2\)-approximations of periodic functions by trigonometric polynomials, the results on the best \(L_2\)-approximations of functions given on the real line by entire functions of the exponential type, and also similar results for almost periodic functions.