Estimates of Best Approximation and Fourier Transforms in Integral Metrics Original Research Article

Under some assumptions on a function F and its Fourier transform F̂ we prove new estimates of best approximation of F by entire functions of exponential type σ in Lp(R), 1 ≤ p < 2. The proof is based on some inequalities for F̂ in L1(R) which may be treated as generalizations of results of Bausov and Telyakovskii. As an application we obtain exact estimates of best approximation of some infinitely differentiable functions.