Approximation by interpolation trigonometric polynomials in metrics of the spaces L_p on the classes of periodic entire functions

2018/06/07 by A. S. Serdyuk, Serdyuk, A. S., И. В. Соколенко +1
Mathematics · #Meromorphic and Entire Functions #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.1806.02561

Abstract

We obtain the asymptotic equalities for the least upper bounds of approximations by interpolation trigonometric polynomials with the equidistant nodes x_k^(n-1)=(2kπ)/(2n-1), k∈ℤ, in metrics of the spaces L_p on classes of 2π-periodic functions, representable as convolutions of functions φ, φ⊥1, which belongs to the unit ball of the space L₁, and fixed generating kernels in the case where modules of their Fourier coefficients ψ(k) satisfy the condition lim_k→∞ ψ(k+1)/ψ(k)=0. We obtain similar estimates on the classes of r-differentiable functions W^r₁ for the quickly increasing exponents of smoothness r (r/n→∞).

Related

• Estimates of approximations by interpolation trigonometric polynomials on the classes of convolutions of high smoothness
• Asymptotic behavior of best approximations of classes of infinitely differentiable functions defined by moduli of continuity
• Approximation of generalized Poisson integrals by interpolation trigonometric polynomials
• Approximation by linear methods of classes of (ψ,β)-differentiable functions
• Order estimates of the best n-term orthogonal trigonometric approximations of the classes \cal F_q^ψ of periodic functions in the integral metrics