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Some remarks on nearness problems for continued fraction expansions

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Analytic Theory of Continued Fractions III

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1406))

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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. 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).

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  2. 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.

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  3. 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.

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  4. O. Njåstad and H. Waadeland, Strongly bounded functions and corresponding PC-fractions, (to appear).

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  5. H. Waadeland, General T-fractions corresponding to functions satisfying certain boundedness conditions, Journal of Approximation Theory 26 (1979), 317–328.

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  6. H. Waadeland, Some properties of general T-fractions, Dept. of Mathematics, University of Trondheim, Norway 5 (1978).

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Author information

Authors and Affiliations

  1. Division of Mathematical Sciences, The University of Trondheim NTH, N-7034, Trondheim-NTH, Norway

    Olav Njåstad

  2. Department of Mathematics and Statistics, The University of Trondheim AVH, N-7055, Dragvoll, Norway

    Haakon Waadeland

Authors
  1. Olav Njåstad
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  2. Haakon Waadeland
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Editor information

Lisa Jacobsen

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© 1989 Springer-Verlag

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Njåstad, O., Waadeland, H. (1989). Some remarks on nearness problems for continued fraction expansions. In: Jacobsen, L. (eds) Analytic Theory of Continued Fractions III. Lecture Notes in Mathematics, vol 1406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0096169

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  • DOI: https://doi.org/10.1007/BFb0096169

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51830-3

  • Online ISBN: 978-3-540-46820-2

  • eBook Packages: Springer Book Archive

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