Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-05-18T08:29:10.723Z Has data issue: false hasContentIssue false
  • English
  • Français

A method for Fourier transforms

Published online by Cambridge University Press:  24 October 2008

R. Kaufman
R. Kaufman
Affiliation:
University of Illinois
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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