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1991 | 62 | 1 | 67-71
Tytuł artykułu

A Helson set of uniqueness but not of synthesis

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In [3] I showed that there are Helson sets on the circle 𝕋 which are not of synthesis, by constructing a Helson set which was not of uniqueness and so automatically not of synthesis. In [2] Kaufman gave a substantially simpler construction of such a set; his construction is now standard. It is natural to ask whether there exist Helson sets which are of uniqueness but not of synthesis; this has circulated as an open question. The answer is "yes" and was also given in [3, pp. 87-92] but seems to have got lost in the depths of that rather long paper. Furthermore, the proof depends on the methods of [3], which few people would now wish to master. The object of this note is to give a proof using the methods of [2].
Słowa kluczowe
Rocznik
Tom
62
Numer
1
Strony
67-71
Opis fizyczny
Daty
wydano
1991
otrzymano
1990-08-30
Twórcy
  • Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, England
Bibliografia
  • [1] J.-P. Kahane, Séries de Fourier Absolument Convergentes, Springer, 1970.
  • [2] R. Kaufman, M-sets and distributions, Astérisque 5 (1973), 225-230.
  • [3] T. W. Körner, A pseudofunction on a Helson set. I, ibid., 3-224.
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Bibliografia
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bwmeta1.element.bwnjournal-article-cmv62i1p67bwm
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