Khrushchev, SergeyGolinskii, LKhrushchev, SMathematics2024-07-052024-07-05200270021-904510.1006/jath.2001.36552-s2.0-0036272481https://doi.org/10.1006/jath.2001.3655https://hdl.handle.net/20.500.14411/1115Khrushchev, Sergey/0000-0002-8854-5317; Golinskii, Leonid/0000-0002-7677-1210The convergence in L-2(T) of the even approximants of the Wall continued fractions is extended to the Cesaro-Nevai class CN, which is defined as the class of probability measures sigma with lim(n-->infinity) 1/n Sigma(k=0)(n-1) \a(k)\ = 0, (a(n))(ngreater than or equal to0) being the Geronimus parameters of sigma. We show that CN contains universal measures, that is, probability measures for which the sequence (\phi(n)\(2) dsigma)(ngreater than or equal to0) is dense in the set of all probability measures equipped with the weak-* topology. We also consider the "opposite" Szego class which consists of measures with Sigma(n=0)(infinity) (1-\a(n)\(2))(1/2) < infinity and describe it in terms of Hessenberg matrices. (C) 2002 Elsevier Science (USA).eninfo:eu-repo/semantics/openAccessunit circle orthogonal polynomialsSchur functionsSchur parametersstrong summabilityArticleQ21152187237WOS:000175919600001