Hostname: page-component-77c89778f8-gvh9x Total loading time: 0 Render date: 2024-07-17T03:55:57.284Z Has data issue: false hasContentIssue false
  • English
  • Français

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: ccgraham@alum.mit.edu
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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