Approximation of classes B_{p,\theta }^r of periodic functions of one and several variables |
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Authors: | A S Romanyuk |
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Institution: | 1. Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev, Ukraine
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Abstract: | We obtain order-sharp estimates of best approximations to the classes $B_{p,\theta }^r$ of periodic functions of several variables in the space L q , 1 ≤ p, q ≤ ∞ by trigonometric polynomials with “numbers” of harmonics from step hyperbolic crosses. In the one-dimensional case, we establish the order of deviation of Fourier partial sums of functions from the classes $ B_{1,\theta }^{r_1 } $ in the space L 1. |
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