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Some remarks on nearness problems for continued fraction expansions

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

Abstract

In some cases “nearness” between functions implies “nearness” between their possible continued fraction expansions of some type. This of course depends strongly upon the way “nearness” between functions is defined, but also upon the choice of function to be “near”. The present note is a brief, informal and example-based discussion of this matter.

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References

  1. 1.
    L. Jacobsen and H. Waadeland, A result on nearness of functions and their regular C-fraction expansions, Proc. of the Amer. Math. Soc. 105 4 (1989).Google Scholar
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    W. B. Jones, O. Njåstad and W. J. Thron, Continued fractions associated with the trigonometric and other strong moment problems, Constructive Approximation 2 (1986), 197–211.MathSciNetCrossRefzbMATHGoogle Scholar
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    W. B. Jones and W. J. Thron, “Continued Fractions: Analytic Theory and Applications. Encyclopedia Math. Appl. 11.,” Addison-Wesley Publ. Co., Reading, Mass., distributed now by Cambridge University Press, New York, 1980.Google Scholar
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    O. Njåstad and H. Waadeland, Strongly bounded functions and corresponding PC-fractions, (to appear).Google Scholar
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    H. Waadeland, General T-fractions corresponding to functions satisfying certain boundedness conditions, Journal of Approximation Theory 26 (1979), 317–328.MathSciNetCrossRefzbMATHGoogle Scholar
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    H. Waadeland, Some properties of general T-fractions, Dept. of Mathematics, University of Trondheim, Norway 5 (1978).Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Olav Njåstad
    • 1
  • Haakon Waadeland
    • 2
  1. 1.Division of Mathematical SciencesThe University of Trondheim NTHTrondheim-NTHNorway
  2. 2.Department of Mathematics and StatisticsThe University of Trondheim AVHDragvollNorway

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