The norm of a minimal linear projection in \(C[0,\infty)\) (Q1589118)

Let \(L_n\) be the operator which assigns to each function \(F\in C[0,\infty)\) its Lagrange interpolating polynomial constructed by using the zeros of a certain polynomial given by means of Laguerre polynomials. Under the assumption that the linear space \(C[0,\infty)\) is endowed with the norm defined by \[ \|F\|= \sup_{x\geq 0}x^{\alpha/2} \bigl|F(x)\bigr|e^{-x/2}, \] where \(\alpha\geq 0\) is a fixed parameter, the author proves that the norm of \(L_n\) satisfies the equality \(\|L_n\|=O(\ln n)\).