Remarks on Theorems of Muntz-Szasz Type

Abstract

function on the interval [0, 1] with φ(0)=0 and let {n(k):k=1,2,...} be a strictly increasing sequence of positive real numbers tending to infinity. Then we have the following: (a) Let C0[0, 1] be the space of (real-or complex-valued) continuous functions on [0, 1] vanishing at 0, equipped with the usual uniform norm. Then, the system {φn(k):k=1,2,...} is fundamental in C0[0, 1] if and only if Σ ∞k=1η(k)-1=