On the Method of Approximation by Families of Linear Polynomial Operators

Abstract

It is shown that best approximation by trigonometric polynomials is achieved in average by families of linear polynomial operators in the $L_p$-metric for all $p,0<p<\infty$. This is compared with approximation by Fourier means and interpolation means which is restricted to $1\le p\le \infty$ and $p=\infty$, respectively.