Singularly Continuous Measures in Nevai's Class M

D. S. Lubinsky
1991 Proceedings of the American Mathematical Society  
Let dv be a nonnegative Borel measure on \-n, n], with 0 < f*n du < co and with support of Lebesgue measure zero. We show that there exist {Vj}%¡ C (0, oo) and {tj}jZ\ C (-it, n) such that if 00 dß (6) :=Y/1jdu(d + tj), 6 e[-n , ti], j=i (with the usual periodic extension dv(d ± 2n) = dv (6) ), then the leading coefficients {Kn(dß)}^L0 of the orthonormal polynomials for dß satisfy \im>K"(dp)/Kn+x(dp)= 1. As a consequence, we obtain pure singularly continuous measures da on [-1,1] lying in
more » ... 1,1] lying in Nevai's class M .
doi:10.2307/2048330 fatcat:mn3dbsaajbb3lhivpf7ew6fobi