Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-29T19:33:49.197Z Has data issue: false hasContentIssue false
  • English
  • Français

Uniform approximation by Fourier–Stieltjes transforms†

Published online by Cambridge University Press:  24 October 2008

Donald E. Ramirez
Donald E. Ramirez
Affiliation:
University of Washington, University of Virginia
Get access Rights & Permissions [Opens in a new window]

Extract

Let G be a locally compact Abelian group; Γ the dual group of G; CB(Γ) the algebra of continuous, bounded functions on Γ C0(Γ) the algebra of continuous functions on Γ which vanish at infinity; M(G) the algebra of bounded Borel measures on G; M(G)^ the algebra of Fourier–Stieltjes transforms; and M(G)^− the completion of M(G)^ in the sup-norm topology on Γ. The object of this paper is to study the natural pairing between M(G)^ and M(Γ).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 2 , April 1968 , pp. 323 - 333
Copyright
Copyright © Cambridge Philosophical Society 1968

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)Bourbaki, N.Espaces vectoriels topologiques, Ch. III–V (Hermann, Paris, France, 1964).Google Scholar
(2)Buck, R. C.Bounded continuous functions on a locally compact space. Michigan Math. J. 5 (1958), 95–104.CrossRefGoogle Scholar
(3)Day, M.Normed linear spaces (second printed corrected). (Academic Press Inc., New York, N.Y. 1962).CrossRefGoogle Scholar
(4)Dunford, N. and Schwartz, J.Linear operators, Part I. (Interscience Publishers, New York, N.Y. 1958).Google Scholar
(5)Edwards, R. E.Uniform approximation on non-compact spaces. Trans. Amer. Math. Soc. 122 (1966), 249–276.CrossRefGoogle Scholar
(6)Hewitt, E. A survey of abstract harmonic analysis. Abstract harmonic analysis, surveys in applied mathematics. IV, pp. 105–168 (J. Wiley and Sons, Inc, 1958).Google Scholar
(7)Köthe, G.Topologische lineare raume I. (Springer-Verlag, Berlin, 1960).CrossRefGoogle Scholar
(8)Rickart, C.General theory of Banach algebras (D. Van Nostrand Company, Inc, Princeton, 1960).Google Scholar
(9)Rudin, W.Fourier analysis on groups (Interscience Publishers, New York, N.Y, 1962).Google Scholar
(10)Rudin, W.Trigonometric series with gaps. J. Math. Mech. 9 (1960), 203–228.Google Scholar
(11)Zygmund, A.Trigonometric series (Cambridge University Press, New York, N.Y., 1959).Google Scholar