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The support of pseudomeasures on

Published online by Cambridge University Press:  12 February 2007

COLIN C. GRAHAM
COLIN C. GRAHAM*
Affiliation:
Department of Mathematics, University of British Columbia, Mailing address: RR#1–H-46, Bowen Island, BC, V0N 1G0Canada. e-mail: [email protected]
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Abstract

PM(E) denotes the set of pseudomeasures on with support in the closed set E ⊆ . Then y ∈ is not in E if and only if there is a neighbourhood W of y with uniformly for w ∈ W and S ∈ PM(E) with ‖S‖PM ≤ 1. This improves previous results by adding “uniformly” and its scope. The proof uses the fact that squashing the central spike of the Fejer kernel leads to A-norm convergence.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 142 , Issue 1 , January 2007 , pp. 149 - 152
Copyright
Copyright © Cambridge Philosophical Society 2007

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References

REFERENCES

[1] González Vieli, F. J.. Intégrales trigonométriques et pseudofonctions. Ann. Inst. Fourier (Grenoble) 44 (1994), no. 1, 197–211.CrossRefGoogle Scholar
[2] González Vieli, F. J.. Inversion de Fourier ponctuelle des distributions à support compact. Arch. Math. 75 (2002), 290–298.CrossRefGoogle Scholar
[3] González Vieli, F. J.. Characterization of the sup-port of pseu-do-mea-sures on . Math. Proc. Camb. Phil. Soc. 135 (2003), 431–442.Google Scholar
[4] Kahane, J.-P. and Salem, R.. Ensembles Parfaits et Séries Trigonométriques (Hermann, 1963). (Nouvelle Édition, 1994.)Google Scholar
[5] Waterloo Maple Software. Maple 7, Windows Version (2001).Google Scholar
[6] Walter, G.. Pointwise convergence of distribution expansions. Studia Math. 26 (1966), 143–154.CrossRefGoogle Scholar