Bases of the space of continuous functions

In this paper, new bases for the space of continuous functions are constructed, similar to the Schauder basis but having better differentiability properties. The bases constructed are applied to the problem of the order of growth of the degrees of a polynomial basis of the space $C(0,1)$. It is proved that for any nondecreasing sequence of natural numbers $\{\omega(n)\}_{n=0}^\infty$ satisfying the condition $\sum_{n=2}^{\infty}\frac1{n\ln n\omega(n)}<\infty$ it is possible to construct a polynomial basis with order of growth $\nu_n\leqslant n\omega(n)$, $n=0,1,2,\dots$ .
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