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A Note on Characteristic Functions Which Vanish Identically in an Interval

Published online by Cambridge University Press:  24 October 2008

Walter L. Smith
Walter L. Smith
Affiliation:
Department of Statistics University of North Carolina
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Extract

Some years ago, in connexion with some unpublished work in the theory of queues, the question arose as to whether the characteristic function of a non-negative random variable could vanish identically in an interval. The purpose of this note is to show that such a thing is impossible.

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 2 , April 1962 , pp. 430 - 432
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

REFERENCES

(1)Bieberbach, L.Lehrbuch der Funktionentheorie, II. Bd. 2. Aufl. (B. G. Teubner, Leipzig and Berlin, 1931).Google Scholar
(2)Titchmarsh, E. CTheory of Fourier integrals, (2nd ed.Oxford University Press, 1948).Google Scholar