Let {P.} be a sequence of orthogoual polynomials with respect to the measure d# on the unit circle and let 7vn = P. + Y']~=I A,,jP._j for n _> l. where A.j E C. It is shown that the sequence of linear combinations {7~.}, n >_ 2/, is orthogonal with respect to a positive measure da if and only if &r is a Bernstein-Szeg6 measure and d# is the product of a… (More)