Uniform approximations by Fourier sums on classes of convolutions with generalized Poisson kernels
DOI:
https://doi.org/10.15407/dopovidi2016.11.010Keywords:
asymptotic equality, Fourier sums, generalized Poisson kernels, Kolmogorov—Nikol'skii problemAbstract
We find asymptotic unimprovable equalities for exact upper bounds of approximations by Fourier sums in a uniform metric on the classes of 2π-periodic functions representable in the form of convolutions of functions φ, which belong to unit balls of spaces Lp, with generalized Poisson kernels. For the obtained asymptotic equalities, we introduce the estimate of a remainder, which is expressed in the explicit form via absolute constants and parameters of the problem. This can be useful for practical application.
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