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A method for Fourier transforms

Published online by Cambridge University Press:  24 October 2008

R. Kaufman
R. Kaufman
Affiliation:
University of Illinois
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Extract

0. Our aim in this note is to obtain theorems about measures, perfect sets, and transforms in the group G of p-adic integers (for a prime p), related to recent developments in compact Abelian groups (6, 7) and again to Fourier analysis in Euclidean space (2–5).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 3 , May 1970 , pp. 619 - 623
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Hewitt, E. and Ross, K. A.Abstract harmonic analysis I (Springer-Verlag, Berlin, 1963)Google Scholar
(2)Kahane, J.-P.Images browniennes des ensembles parfaits. C.R. Acad. Sci. Paris Ser. A 263 (1966), 613–615. Images d'ensembles parfaits par des series de Fourier gaussiennes. C.R. Acad. Sci. Paris Ser A, 678–681.Google Scholar
(3)Kaufman, R.Measures in independent sets. Studia Math. 30 (1968), 17–20.CrossRefGoogle Scholar
(4)Rudin, W.Fourier-Stieltjes transforms of measures on independent sets. Bull. Amer. Math. Soc. 64 (1958), 199–200.Google Scholar
(5)Salem, R.On singular monotonic functions whose spectrum has a given Hausdorff dimension. Ark. Mat. 1 (1951), 353–365.CrossRefGoogle Scholar
(6)Varopoulos, N. Th.Sets of multiplicity in locally compact abelian groups. Ann. Inst. Fourier (Grenoble) 16 (1966), 123–158.CrossRefGoogle Scholar
(7)Walker, P. L.Lipschitz classes on O-dimensional groups. Proc. Cambridge Philos. Soc. 63 (1967), 923–928.CrossRefGoogle Scholar