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Convergence of the Schur algorithm


Author: Olav Njåstad
Journal: Proc. Amer. Math. Soc. 110 (1990), 1003-1007
MSC: Primary 30B70; Secondary 40A15
DOI: https://doi.org/10.1090/S0002-9939-1990-1028292-2
MathSciNet review: 1028292
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Abstract: Convergence of the Schur algorithm outside the unit circle is discussed with the aid of convergence theory for Schur continued fractions.


References [Enhancements On Off] (What's this?)

  • [1] W. B. Jones, O. Njåstad, and W. J. Thron, Schur fractions, Perron-Carathéodory fractions and Szegö polynomials, a survey, in Analytic Theory of Continued Fractions II (W. J. Thron, ed.), Lecture Notes in Math., vol. 1199, Springer-Verlag, New York, 1986, pp. 127-158. MR 870247 (88b:30005)
  • [2] -, Moment theory, orthogonal polynomials, quadrature, and continued fractions associated with the unit circle, Bull. London Math. Soc. 21 (1989), 113-152. MR 976057 (90e:42027)
  • [3] W. B. Jones and W. J. Thron, Continued fractions: analytic theory and applications, Encyclopedia of Mathematics and its Applications, vol. 11, Addison-Wesley, 1980 (distributed now by Cambridge University Press). MR 595864 (82c:30001)
  • [4] O. Njåstad, A survey of some results on separate convergence of continued fractions, in Analytic Theory of Continued Fractions III (L. Jacobsen, ed.), Lecture Notes in Math., vol. 1406, Springer-Verlag, New York, 1989, pp. 88-114. MR 1034964 (91b:30016)
  • [5] H-J. Runckel, Bounded analytic functions in the unit disk and the behavior of certain analytic continued fractions near the singular line, J. Reine Angew. Math. 281 (1976), 97-125. MR 0393444 (52:14254)
  • [6] I. Schur, Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind, J. Reine Angew. Math. 147 (1916), 205-232; 148 (1917), 122-145.
  • [7] H. S. Wall, Continued fractions and bounded analytic functions, Bull. Amer. Math. Soc. 50 (1944), 110-119. MR 0010211 (5:262e)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1028292-2
Keywords: Schur algorithm, Schur continued fractions
Article copyright: © Copyright 1990 American Mathematical Society

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