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Random recursive construction of Salem sets

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Arkiv för Matematik

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Abstract

We introduce a random recursive method for constructing random Salem sets inR d. The method is inspired by Salem's construction [13] of certain signular monotonic functions.

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References

  1. Bluhm, C., Zufällige Salem-Mengen, Master's thesis, Erlangen, 1994.

  2. Bluhm, C., Zur Konstruktion von Salem-Mengen, Forthcoming doctoral thesis, Erlangen, 1996.

  3. Falconer, K. J.,Fractal Geometry. Mathematical Foundations and Applications, J. Wiley & Sons, Chichester, 1990.

    MATH  Google Scholar 

  4. Frostman, O., Potential d'équilibre et capacité des ensembles avec quelques applications à la théorie des fonctions,Medd. Lunds Univ. Math. Sem. 3 (1935) 1–118.

    Google Scholar 

  5. Graf, S., Statistically self-similar fractals,Probab. Theor. Relat. Fields 74 (1987), 357–392.

    Article  MathSciNet  Google Scholar 

  6. Hurewicz, W. andWallman, H.,Dimension Theory, Princeton University Press, Princeton, N. J., 1941.

    Google Scholar 

  7. Kahane, J.-P., Brownian motion and classical analysis,Bull. London Math. Soc. 8 (1976), 145–155.

    MathSciNet  Google Scholar 

  8. Kahane, J.-P.,Some Random Series of Functions, Cambridge University Press, 2nd ed., Cambridge, 1985.

  9. Kechris, A. S. andLouveau, A., Descriptive set theory and harmonic analysis,J. Symbolic Logic 57 (1992), 413–441.

    Article  MathSciNet  Google Scholar 

  10. Matheron, G.,Random Sets and Integral Geometry, J. Wiley & Sons, New York-London, 1975.

    MATH  Google Scholar 

  11. Mauldin, R. D. andWilliams, S. C., Random recursive constructions: asymptotic geometric and topological properties.Trans. Amer. Math. Soc. 295 (1986), 325–346.

    Article  MathSciNet  Google Scholar 

  12. Salem, R., Sets of uniqueness and sets of multiplicity,Trans. Amer. Math. Soc. 54 (1943), 218–228.

    Article  MathSciNet  Google Scholar 

  13. Salem, R., On singular monotonic functions whose spectrum has a given Hausdorff dimension.Ark. Mat. 1 (1950), 353–365.

    MathSciNet  Google Scholar 

  14. Steinhaus, H., Sur la probabilité de la convergence de séries,Studia Math. 2 (1930), 21–39.

    Google Scholar 

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Authors and Affiliations

  1. Mathematisches Institut, Friedrich-Alexander-Universität Erlangen-Nürnberg, Bismarckstrasse 1 1/2, D-91054, Erlangen, Germany

    Christian Bluhm

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  1. Christian Bluhm
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Additional information

This work contains parts of the author's forthcoming doctoral thesis [2] which were presented at theConference on Harmonic Analysis from the Pichorides Viewpoint in Anogia Academic Village on Crete in July 1995.

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Bluhm, C. Random recursive construction of Salem sets. Ark. Mat. 34, 51–63 (1996). https://doi.org/10.1007/BF02559506

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  • DOI: https://doi.org/10.1007/BF02559506

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