APPROXIMATION BY INTERPOLATION TRIGONOMETRIC POLYNOMIALS IN METRICS OF THE SPACE Lp ON THE CLASSES OF PERIODIC ENTIRE FUNCTIONS

We establish asymptotic equalities for the least upper bounds of approximations by interpolation trigonometric polynomials with equidistant distribution of interpolation nodes x(k)((n-1)) = 2k pi/2n - 1, k is an element of Z, in metrics of the spaces L-p on the classes of 2 pi-periodic functions that can be represented in the form of convolutions of functions phi, phi perpendicular to 1, from the unit ball in the space L-1 with fixed generating kernels in the case where the modules of their Fourier coefficients psi(k) satisfy the condition lim(k ->infinity) psi (k + 1)/psi(k) = 0. Similar estimates are also obtained for the classes of r-differentiable functions W-1(r) with rapidly increasing exponents of smoothness r (r/n -> infinity, n -> infinity).