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On the structure of Sidon sets

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Abstract

LetG be any connected compact group with dual objectĜ. We give in this paper a new proof that the union of any two Sidon sets inĜ is again a Sidon set. We also show that any Sidon subset ofĜ is the union of a set whose elements have bounded degree with a finite union of sets which satisfy a quasi-independence condition.

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References

  1. Bożejko, M. Sidon sets in dual objects of compact groups. Colloq. Math.30, 137–141 (1974).

    Google Scholar 

  2. Cartwright, D. I., McMullen, J. R.: A structural criterion for the existence of infinite Sidon sets. Pacific J. Math.96, 301–317 (1981).

    Google Scholar 

  3. Hewitt, E., Ross, K. A.: Abstract Harmonic Analysis, Vol. I, 2nd ed. Berlin-Heidelberg-New York: Springer. 1979.

    Google Scholar 

  4. Hewitt, E., Ross, K. A.: Abstract Harmonic Analysis, Vol. II, Berlin-Heidelberg-New York: Springer. 1970.

    Google Scholar 

  5. Hutchinson, M. F.: Lacunary sets for connected and totally disconnected compact groups. Ph.D. thesis. University of Sydney. 1977; abstracted in Bull. Austral. Math. Soc.,18, 149–151 (1978).

  6. Marcus, M. B., Pisier, G.: Random Fourier Series with Applications to Harmonic Analysis. Princeton: Princeton Univ. Press and Univ. of Tokyo Press. 1981.

    Google Scholar 

  7. Parker, W. A.: Central Sidon and central Λ p sets. J. Austral. Math. Soc.14, 62–74 (1972).

    Google Scholar 

  8. Pisier, G.: De nouvelles caractérisations des ensembles de Sidon. Adv. Math.7B, 685–726 (1981).

    Google Scholar 

  9. Pisier, G.: Arithmetic characterizations of Sidon sets. Bull. Amer. Math. Soc.8, 87–89 (1983).

    Google Scholar 

  10. Price, J. F.: Lie groups and compact groups. London Math. Soc. Lec. Note Ser., No. 25. Cambridge-London-New York-Melbourne: Cambridge Univ. Press. 1977.

    Google Scholar 

  11. Rider, D.: Randomly continuous functions and Sidon sets. Duke Math. J.42, 759–764 (1975).

    Google Scholar 

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Wilson, D.C. On the structure of Sidon sets. Monatshefte für Mathematik 101, 67–74 (1986). https://doi.org/10.1007/BF01326848

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  • DOI: https://doi.org/10.1007/BF01326848

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