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 polynomialswith equidistant distribution of interpolation nodes $x_{(n 1)}^k = \frac{2k\pi}{2n 1}, k \in Z,$, in metrics of the spaces $L_p$ on the classesof $2\pi$ -periodic functions that can be represented in the form of convolutions of functions $\varphi , \varphi \bot 1$, from the unit ball ofthe space $L_1$, with fixed generating kernels in the case where the modules of their Fourier coefficients $\psi (k)$ satisfy thecondition $\mathrm{lim}_{k\rightarrow \infty} \psi (k + 1)/\psi (k) = 0.$. Similar estimates are also obtained on the classes of $r$-differentiable functions$W^r_1$ for the rapidly increasing exponents of smoothness $r (r/n \rightarrow \infty , n \rightarrow \infty )$.