2015arXiv (Cornell University)Open access

Estimates for approximations by Fourier sums, best approximations and best orthogonal trigonometric approximations of the classes of (\psi, \beta)-differentiable functions

A. S. Serdyuk, Тетяна Степанюк

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Abstract

We obtain the exact-order estimates for approximations by Fourier sums, best approximations and best orthogonal trigonometric approximations in metrics of spaces L_s, 1\leq s<\infty, of classes of 2\pi-periodic functions, whose (\psi,\beta)-derivatives belong to unit ball of the space L_\infty.

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We obtain the exact-order estimates for approximations by Fourier sums, best approximations and best orthogonal trigonometric approximations in metrics of spaces L_s, 1\leq s<\infty, of classes of 2\pi-periodic functions, whose (\psi,\beta)-derivatives belong to unit ball of the space L_\infty.

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Available abstract

We obtain the exact-order estimates for approximations by Fourier sums, best approximations and best orthogonal trigonometric approximations in metrics of spaces L_s, 1\leq s<\infty, of classes of 2\pi-periodic functions, whose (\psi,\beta)-derivatives belong to unit ball of the space L_\infty.

Key concepts: Approximations of π, Mathematics, Trigonometry, Differentiable function, Fourier series, Fourier transform, Space (punctuation), Mathematical analysis

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