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The Wiener-Pitt Phenomenon on the Half-Line

Published online by Cambridge University Press:  20 January 2009

J. H. Williamson
J. H. Williamson
Affiliation:
King's College, Cambridge
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It has been well known for many years (2) that if Fμ(t) is the Fourier-Stieltjes transform of a bounded measure μ on the real line R, which is bounded away from zero, it does not follow that [Fμ(t)]−1 is also the Fourier-Stieltjes transform of a measure. It seems of interest (as was remarked, in conversation, by J. D. Weston) to consider measures on the half-line R+ = [0, ∞[, instead of on R.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 13 , Issue 1 , June 1962 , pp. 37 - 38
Copyright
Copyright © Edinburgh Mathematical Society 1962

References

REFERENCES

(1) Rudin, W., Bull. American Math. Soc., 65 (1959), 227–247.CrossRefGoogle Scholar
(2) Wiener, N. and Pitt, H. R., Duke Math. J., 4 (1938), 420–436.Google Scholar
(3) Williamson, J. H., Communication at International Congress of Mathematicians (Edinburgh, 1958).Google Scholar
(4) Williamson, J. H., Proc. Edin. Math. Soc., 11 (1959), 195–206.CrossRefGoogle Scholar