A Helson set of uniqueness but not of synthesis

• Autorzy: T. W. Körner
• Języki publikacji: EN

Abstrakty

EN

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].

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1991
• Tom: 62
• Numer: 1
• Strony: 67-71

Daty

wydano

1991

otrzymano

1990-08-30

Twórcy

autor

T. W. Körner

• 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.