Hostname: page-component-5c6d5d7d68-wpx84 Total loading time: 0 Render date: 2024-08-19T02:59:49.669Z Has data issue: false hasContentIssue false
  • English
  • Français

Probability measures with trivial Stam groups

Published online by Cambridge University Press:  24 October 2008

Gavin Brown  and
William Mohan
Gavin Brown
Affiliation:
University of New South Wales
William Mohan
Affiliation:
University of Adelaide
Get access Rights & Permissions [Opens in a new window]

Extract

Let μ be a probability measure on the real line ℝ, x a real number and δ(x) the probability atom concentrated at x. Stam made the interesting observation that either

or else

(ii) δ(x)* μn, are mutually singular for all positive integers n.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 91 , Issue 3 , May 1982 , pp. 477 - 484
Copyright
Copyright © Cambridge Philosophical Society 1982

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)Brown, G.Riesz products and generalized characters. Proc. London Math. Soc. 30 (1975), 209–238.Google Scholar
(2)Brown, G. and Moran, W.On orthogonality of Riesz products. Proc. Cambridge Philos. Soc. 76 (1974), 173–181.CrossRefGoogle Scholar
(3)Brown, G. and Moran, W.Point derivations on M(G). Butt. London Math. Soc. 8 (1976), 57–64.CrossRefGoogle Scholar
(4)Fourt, G.Existence de measures à puissances singulières à toutes leurs translaées. C. R. Acad. Sci. Paris, Sér A-B, 274 (1972), 4648–650.Google Scholar
(5)Heyer, H.Probability measures on locally compact groups (Springer-Verlag, Berlin, Heidelberg, New York, 1977).Google Scholar
(6)Körner, T. W.Some results on Kronecker, Dirichlet, and Helson sets. Ann. Inst. Fourier. Grenoble 20 (1970), 219–324.Google Scholar
(7)Rudin, W.Fourier-Stieltjes transforms of measures on independent sets. Bull. Amer. Math. Soc. 66 (1960), 199–202.CrossRefGoogle Scholar
(8)Salem, R.Algebraic numbers and Fourier analysis (Heath, Boston, 1963).Google Scholar
(9)Sreider, Yu.A. The structure of maximal ideals in rings of measures with convolution. Mat. Sbornik, N.S. 27, 69 (1950), 297–318. (A.M.S. Translation 81.)Google Scholar