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.
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