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Approximation by Fourier sums on the classes of generalized Poisson integrals https://arxiv.org/abs/2409.10629 #mathCA

Approximation by Fourier sums on the classes of generalized Poisson integrals

We present a survey of results related to the solution of Kolmogorov--Nikolsky problem for Fourier sums on the classes of generalized Poisson integrals $C^{α,r}_{β,p}$, which consists in finding of asymptotic equalities for exact upper boundaries o f uniform norms of deviations of partial Fourier sums on the classes of $2π$--periodic functions $C^{α,r}_{β,p}$, which are defined as convolutions of the functions, which belong to the unit balls pf the spaces $L_{p}$, $1\leq p\leq \infty$, with generalized Poisson kernels $$ P_{α,r,β}(t)=\sum\limits_{k=1}^{\infty}e^{-αk^{r}}\cos \big(kt-\frac{βπ}{2}\big), \ α>0, r>0, \ β\in \mathbb{R}.$$

arxiv.org
September 19, 2024 at 3:10 AM · · feed2toot · 0 · 0 · 0
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