Jackson and Bernstein theorems for the weight \(\exp(-|x|)\) on \(\mathbb R\) (Q2480556)

The author obtains Bernstein's and Jackson's type theorems, generalizing the results obtained in 1978 by \textit{G. Freud, A. Giroux} and \textit{Q. I. Rahman} [Can. J. Math. 30, 358--372 (1978; Zbl 0409.41002)], using a substantially modified technique. He involves approximating the function by a spline representing the piecewise polynomial in terms of certain characteristic functions and then approximating the characteristic functions by polynomials. For the rate of approximation, a moduli of continuity is introduced and used.