Orthogonal Newton polynomials

AbstractThe problem is to determine all nonnegative measures on the Borel subsets of the complex plane with respect to which all polynomials are square integrable and with respect to which the Newton polynomials form an orthogonal set. The Newton polynomials do not belong to any classical scheme of orthogonal polynomials. The discovery that a plane measure exists with respect to which they form an orthogonal set was only recently made by T. L. Kriete and D. Trutt [Amer. J. Math.93 (1971), 215–225]. A general structure theory for such measures is now obtained under hypotheses suggested by the expansion theory of Cesàro operators