SINGULARLY CONTINUOUS MEASURES IN NEVAIS CLASS-M

Let d-nu be a nonnegative Borel measure on [-pi, pi], with 0 < integral-pi-pi d-nu < infinity and with support of Lebesgue measure zero. We show that there exist {eta-j}j infinity = 1 subset-of (0, infinity) and {t(j)}j infinity = 1 subset-of (-pi, pi) such that if [GRAPHICS] (with the usual periodic extension d-nu-(theta +/- 2-pi) = d-nu-(theta)), then the leading coefficients {k(n)(d-mu)}n infinity = 0 of the orthonormal polynomials for d-mu satisfy [GRAPHICS] As a consequence, we obtain pure singularly continuous measures d-alpha on [-1,1] lying in Nevai's class M.