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Article Citation - WoS: 1Citation - Scopus: 2Turan measures(Academic Press inc Elsevier Science, 2003) Khrushchev, SA probability measure a on the unit circle T is called a Turan measure if any point of the open unit disc D is a limit point of zeros of the orthogonal polynomials associated to a. We show that many classes of measures, including Szego measures, measures with absolutely convergent series of their parameters, absolutely continuous measures with smooth densities, contain Turan measures. (C) 2003 Elsevier Science (USA). All rights reserved.Article Citation - WoS: 4Citation - Scopus: 3The Euler-Lagrange Theory for Schur's Algorithm: Wall Pairs(Academic Press inc Elsevier Science, 2006) Khrushchev, SThis paper develops a techniques of Wall pairs for the study of periodic exposed quadratic irrationalities in the unit ball of the Hardy algebra. (C) 2005 Elsevier Inc. All rights reserved.Article Citation - WoS: 5Citation - Scopus: 5The Euler-Lagrange Theory for Schur's Algorithm: Algebraic Exposed Points(Academic Press inc Elsevier Science, 2006) Khrushchev, SIn this paper the ideas of Algebraic Number Theory are applied to the Theory of Orthogonal polynomials for algebraic measures. The transferring tool are Wall continued fractions. It is shown that any set of closed arcs on the circle supports a quadratic measure and that any algebraic measure is either a Szego measure or a measure supported by a proper subset of the unit circle consisting of a finite number of closed arcs. Singular parts of algebraic measures are finite sums of point masses. (C) 2005 Elsevier Inc. All rights reserved.
