Approximation by interpolation trigonometric polynomials on classes of periodic analytic functions - Serdyuk, A. S. (Ukrains’kyi Matematychnyi Zhurnal, 2012)
We establish asymptotically unimprovable interpolation analogs of Lebesgue-type inequalities on the sets C^ψ_βL_p of (ψ, β)-differentiable functions generated by sequences ψ(k) that satisfy the d’Alembert conditions. We find asymptotic equalities for the least upper bounds of approximations by interpolation trigonometric polynomials on the classes C^ψ_β, p, 1 ≤ p ≤ ∞.