  The Hardy operator has all the monomial functions as eigenvectors. We study
bounded operators on L^2 that take monomial functions to multiples of other
monomials, with a shifted exponent. We prove that they all leave the space of
functions vanishing on [0,s] invariant. We prove an asymptotic Muntz-Szasz
theorem, characterizing the set of functions that are limits of linear
combinations of monomials with exponents between n and 2n.
