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Unbounded operators and random Fourier series

Published online by Cambridge University Press:  24 October 2008

J. W. Sanders
Affiliation:
Australian National University

Extract

0·0. Let G be an infinite compact abelian group with dual X. Parseval's identity shows that if fC(G) and ω ∈ l(X) then . Edwards has shown in (2) that L2(G) here cannot, in general, be replaced by any smaller Lp(G) space. Precisely: there exist fC(G) and ω: X → {± 1} such that . We strengthen this result by showing much more can be said about the summability of the Fourier series of f than . For example, when G is the circle group, f can be chosen to also satisfy

The functions introduced here and called darts, generalize this type of series condition.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

REFERENCES

(1)Edwards, R. E.Functional analysis. Theory and applications (New York; Holt, Rinehart and Winston, Inc., 1965).Google Scholar
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(5)Sanders, J. W.Weighted Sidon sets. Pacific J. Math. (to appear).Google Scholar