Advertisement

A survey of some results on separate convergence of continued fractions

  • Olav Njåstad
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1406)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Geronimus, Ya.L: Polynomials orthogonal on a circle and their applications, Amer.Math.Soc., Translation Number 104, Providence (1954).Google Scholar
  2. 2.
    Geronimus, Ya.L.: Orthogonal Polynomials, Consultants Bureau, New York (1961).zbMATHGoogle Scholar
  3. 3.
    Henrici, P.: Applied and Computational Complex Analysis, vol I, Wiley, New York (1974).zbMATHGoogle Scholar
  4. 4.
    Hille, E.: Analytic Function Theory, vol II, Ginn, New York (1962).zbMATHGoogle Scholar
  5. 5.
    Jones, W.B. and Thron, W.J.: Continued Fractions: Analytic Theory and Applications, Encyclopedia of Mathematics and its Applications, 11, Addison-Wesley, Reading (1980), distributed now by Cambridge University Press.Google Scholar
  6. 6.
    Jones, W.B., Njåstad, O. and Thron, W.J.: Continued fractions associated with the trigonometric and other strong moment problems, Constructive Approximation 2 (1986) 197–211.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Jones, W.B., Njåstad, O. and Thron, W.J.: Schur fractions, Perron-Carathéodory fractions and Szegö polynomials, a Survey, Analytic Theory of Continued fractions II, W.T. Thron (ed.), Springer Lecture Notes in Mathematics 1199, New York-Berlin (1986) 127–158.Google Scholar
  8. 8.
    Jones, W.B., Njåstad, O. and Thron, W.J.: Moment theory, orthogonal polynomials, quadrature and continued fractions associated with the unit circle, Bull. Lond. Math. Soc., to appear.Google Scholar
  9. 9.
    Runckel, H.: 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.MathSciNetzbMATHGoogle Scholar
  10. 10.
    Runckel, H.: Continurity on the boundary and analytic continuation of continued fractions, Math. Zeitschrift 148 (1976) 189–205.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Schur, I.: Über Potenzreihen, die im Innern des Einheitskreises beschränkt sind, J. Reine Angew. Math. 147 (1916) 205–232, 148(1917) 122–145.MathSciNetzbMATHGoogle Scholar
  12. 12.
    Sleschinsky, J.W.: Über die Convergenz der Kettenbrüche, Odessa. Ges. VIII (1888) 97–127.Google Scholar
  13. 13.
    Sleschinsky, J.W.: Beweis der Existenz einiger Grentzen, Oddessa. Ges. VIII (1888) 127–137.Google Scholar
  14. 14.
    Waadeland, H.: A convergence property of certain T-fraction expansions, Kgl. Norske Videnskabers Selskab, Skrifter No. 9 (1966) 1–22.Google Scholar
  15. 15.
    Wall, H.S.: The behavior of certain Stieltjes continued fractions near the singular line, Bull. Amer. Math. Soc. 51 (1942) 427–431.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Olav Njåstad
    • 1
  1. 1.Department of MathematicsUniversity of Trondheim - NTHTrondheimNorway

Personalised recommendations