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Random Fourier–Stieltjes transforms on partially ordered ǵroups

Published online by Cambridge University Press:  24 October 2008

John Fournier
John Fournier
Affiliation:
University of British Columbia
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Extract

If one changes at random the signs of the Fourier coefficients of an L2 function the result is still the sequence of Fourier coefficients of an L2 function. L2 is the only LP space with this property; in fact if a sequence remains a Fourier transform for every insertion of ± signs then it is really the transform of an L2 function ((6), p. 215, Theorem 8·14). Our main theorem is a version of this principle, for sequences defined on suitable subsets of a group; it is phrased in terms of large sets of choices of ± signs rather than all sequences of ± signs.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 67 , Issue 2 , March 1970 , pp. 295 - 306
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

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