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Changes of signs of restrictions of Fourier–Stieltjes transforms

Published online by Cambridge University Press:  24 October 2008

G. I. Gaudry
G. I. Gaudry
Affiliation:
University of Warwick, Coventry
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Abstract

Our principal result deals with a function φ defined on the ‘non-negative half’ X+ of a discrete ordered group X, the dual of a compact Abelian connected group G. Suppose φ vanishes outside a countable set S = {χ1, χ2 …} and has the following property: for every t in a set 0 ⊂ (0, 1) of positive Lebesgue measure, the function on X+ defined to be 0 off S and to be rn(t)φ(χn) for χ = χn, where rn is the nth Rademacher function, is the restriction to X+ of a Fourier–Stieltjes transform. We conclude that φ ∈ ℓ2(X+).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 2 , September 1969 , pp. 295 - 300
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

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