Estimates of the best orthogonal trigonometric approximations of the classes of convolutions of periodic functions of not high smoothness

DOI10.15407/DOPOVIDI2015.07.013zbMATH Open1340.42005arXiv1410.3858OpenAlexW2334983668MaRDI QIDQ3464175

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Publication date: 20 January 2016

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Abstract: We obtain order estimates for the best uniform orthogonal trigonometric approximations of

2 p i

-periodic functions, whose

-derivatives belong to unit balls of spaces

L_{p}, 1 l e q p < i n f t y

, in case at consequences

p s i (k)

are that product

p s i (n) n^{f r a c 1 p}

can tend to zero slower than any power function and

s u m l i m i t s_{k = 1}^{i n f t y} p s i^{p^{'}} (k) k^{p^{'} - 2} < i n f t y

when

1 < p < i n f t y

,

f r a c 1 p + f r a c 1 p^{'} = 1

and

s u m l i m i t s_{k = 1}^{i n f t y} p s i (k) < i n f t y

when

p = 1

. We also establish the analogical estimates in

L_{s}

-metric,

1 < s l e q i n f t y

, for classes of the summable

-differentiable functions, such that

.

Full work available at URL: https://arxiv.org/abs/1410.3858

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