Khrushchev, Sergey

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https://hdl.handle.net/20.500.14411/8378
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Khrushchev, S
Khrushchev, S.
Khrushchev, SV
S.,Khrushchev
K.,Sergey
K., Sergey
Sergey, Khrushchev
S., Khrushchev
Khrushchev,S.
Khrushchev, Sergey
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Profesör Doktor
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Mathematics
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Former Staff
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Now showing 1 - 10 of 18
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    Article
    Citation - WoS: 1
    Citation - Scopus: 2
    Turan measures
    (Academic Press inc Elsevier Science, 2003) Khrushchev, S
    A 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.
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    Book Part
    Citation - WoS: 4
    Continued Fractions: Real Numbers
    (Cambridge Univ Press, 2008) Khrushchev, Sergey
    [No Abstract Available]
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    Article
    Citation - WoS: 7
    Citation - Scopus: 9
    Cesaro Asymptotics for Orthogonal Polynomials on the Unit Circle and Classes of Measures
    (Academic Press inc Elsevier Science, 2002) Golinskii, L; Khrushchev, S
    The 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).
  • Thumbnail Image
    Book Part
    Continued Fractions: Algebra
    (Cambridge Univ Press, 2008) Khrushchev, Sergey
    [No Abstract Available]
  • Thumbnail Image
    Book Part
    Continued Fractions: Analysis
    (Cambridge Univ Press, 2008) Khrushchev, Sergey
    [No Abstract Available]
  • Thumbnail Image
    Book Part
    Continued Fractions: Euler's Influence
    (Cambridge Univ Press, 2008) Khrushchev, Sergey
    [No Abstract Available]
  • Thumbnail Image
    Editorial
    Orthogonal Polynomials and Continued Fractions From Euler's Point of View Preface
    (Cambridge Univ Press, 2008) Khrushchev, Sergey
    [No Abstract Available]
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    Article
    Citation - WoS: 4
    Citation - Scopus: 3
    The Euler-Lagrange Theory for Schur's Algorithm: Wall Pairs
    (Academic Press inc Elsevier Science, 2006) Khrushchev, S
    This 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.
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    Conference Object
    Citation - WoS: 1
    On Euler's differential methods for continued fractions
    (Kent State University, 2006) Khrushchev, Sergey; Mathematics
    A differential method discovered by Euler is justified and applied to give simple proofs to formulas relating important continued fractions with Laplace transforms. They include Stieltjes formulas and some Ramanujan formulas. A representation for the remainder of Leibniz's series as a continued fraction is given. We also recover the original Euler's proof for the continued fraction of hyperbolic cotangent.
  • Thumbnail Image
    Book Part
    Continued fractions: Euler
    (Cambridge Univ Press, 2008) Khrushchev, Sergey
    [No Abstract Available]