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Mat. Zametki, 2013, Volume 93, Issue 6, Pages 878–901 (Mi mz9288)  

Approximation of Periodic Functions Using $\mathrm{mup}_s(x)$

V. A. Makarichev

National Aerospace University "Kharkiv Aviation Institute"

Abstract: The spaces of linear combinations of the shifts of a compactly supported solution of a functional-differential equation are considered. It is proved that they are asymptotically extremal for approximating, in the norm of $L_2$, functions from the classes $\widetilde{W}_2^r$.

Keywords: approximation of periodic functions, the classes $\widetilde{W}_2^r$, functional-differential equation, the function $mup_s(x)$, basis function, Taylor series, linear operator.

DOI: https://doi.org/10.4213/mzm9288

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English version:
Mathematical Notes, 2013, 93:6, 858–880

Bibliographic databases:

Document Type: Article
UDC: 517
Received: 18.11.2011
Revised: 07.05.2012

Citation: V. A. Makarichev, “Approximation of Periodic Functions Using $\mathrm{mup}_s(x)$”, Mat. Zametki, 93:6 (2013), 878–901; Math. Notes, 93:6 (2013), 858–880

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