Approximation of infinitely differentiable periodic functions by interpolation trigonometric polynomials

  • A. S. Serdyuk


We establish asymptotically unimprovable interpolation analogs of Lebesgue-type inequalities on the classes of periodic infinitely differentiable functions C Ψ β C whose elements can be represented in the form of convolutions with fixed generating kernels. We obtain asymptotic equalities for upper bounds of approximations by interpolation trigonometric polynomials on the classes C Ψ β,∞ and C Ψ β H ω.
How to Cite
Serdyuk, A. S. “Approximation of Infinitely Differentiable Periodic Functions by Interpolation Trigonometric Polynomials”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, no. 4, Apr. 2004, pp. 495–505,
Research articles