Approximation by interpolation trigonometric polynomials in metrics of the spaces L_p on the classes of periodic entire functions - Serdyuk, A. S.; Sokolenko, I. V. (Ukrains’kyi Matematychnyi Zhurnal, 2019)
We obtain the asymptotic equalities for the least upper bounds of approximations by interpolation trigonometric polynomials with equidistant distribution of interpolation nodes x_(n 1)^k = 2kπ2n 1, k Z,, in metrics of the spaces L_p on the classes of 2π -periodic functions that can be represented in the form of convolutions of functions φ , φ 1, from the unit ball of the space L_1, with fixed generating kernels in the case where the modules of their Fourier coefficients ψ (k) satisfy the condition lim_k→ ∞ ψ (k + 1)/ψ (k) = 0.. Similar estimates are also obtained on the classes of r-differentiable functions W^r_1 for the rapidly increasing exponents of smoothness r (r/n → ∞ , n → ∞ ).