Approximation properties of generalized Fup-functions
DOI:
https://doi.org/10.26565/2221-5646-2016-84-06Keywords:
function with a compact support, approximation of periodic functions, up-function, Kolmogorov width, best approximation, generalized Fup-functionAbstract
Generalized Fup-functions are considered. Almost-trigonometric basis theorem is proved. Spaces of linear combinations of shifts of the generalized Fup-functions are constructed and an upper estimate of the best approximation of classes of periodic differentiable functions by these spaces in the norm of $L_2[-\pi,\pi]$ is obtained.
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