On the orders of the best approximations of integrals of functions by integrals of rank σ |
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Authors: | A I Stepanets and A L Shidlich |
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Institution: | (1) Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev, Ukraine |
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Abstract: | We study the values e
σ(f) of the best approximation of integrals of functions from the spaces L
p
(A, dμ) by integrals of rank σ. We determine the orders of the least upper bounds of these values as σ → ∞ in the case where the function ƒ is the product of two nonnegative functions one of which is fixed and the other varies
on the unit ball U
p
(A) of the space L
p
(A, dμ). We consider applications of the obtained results to approximation problems in the spaces S
p
ϕ.
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Translated from Neliniini Kolyvannya, Vol. 10, No. 4, pp. 528–559, October–December, 2007. |
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Keywords: | |
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