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Fourier transforms and descriptive set theory

Published online by Cambridge University Press:  26 February 2010

R. Kaufman
Affiliation:
Department of Mathematics, University of Illinois, 273 Altgeld Hall, 1409, West Green Street, Urbana, Illinois, 61801, U.S.A.
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Extract

We state some definitions belonging to the two halves of the title, going far enough to state our main results.

Fourier transforms. Let μ be a finite, complex-valued measure on R and its Fourier-Stieltjes transform. We define ℛ to be the set of μ with When μ ∈ ℛ and φ is of class (continuously differentiable of compact support), the identity shows that θ · μ ∈ ℛ.

Type
Research Article
Copyright
Copyright © University College London 1984

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References

1.Engelking, R.. General topology (PWN, Warsaw, 1977).Google Scholar
2.Kaufman, R.. Bernoulli convolutions and differentiable functions. Trans. Amer. Math. Soc, 217 (1976), 99104.CrossRefGoogle Scholar
3.Kaufman, R.. On Bernoulli convolutions. Conference in modern analysis and probability (New Haven, 1982). Contemporary mathematics 26 (Amer. Math. Soc, 1984).Google Scholar
4.Kaufman, R.. Representation of Suslin sets by operators. Manuscript in preparation.Google Scholar
5.Kuratowski, C.. Topologie I, 3rd edition (PWN, Warsaw, 1952). English edition (Academic Press, 1968).Google Scholar
6.Mazurkiewicz, S. et Sierpiński, W.. Sur un probleme concernant les fonctions continues. Fund. Math. 6 (1924), 161169. Also in W. Sierpinski, Oeuvres Choisies, Vol. II, 559-566 (PWN, Warsaw, 1975).CrossRefGoogle Scholar
7.Zygmund, A.. Trigonometric series II (Cambridge University Press, 1959 and 1968).Google Scholar