Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-24T12:51:57.935Z Has data issue: false hasContentIssue false
  • English
  • Français

The Wiener–Pitt phenomenon on semi-groups

Published online by Cambridge University Press:  24 October 2008

T. A. Davis
T. A. Davis
Affiliation:
Trinity Hall, Cambridge
Get access Rights & Permissions [Opens in a new window]

Extract

Let G be a locally compact Abelian group, written adoptively, with Haar measure m, L1(G) the group algebra of G, and M(G) the Banach algebra of all bounded, complex-valued, regular, countably additive measures on G. For a general account of L1(G) and M(G) see Rudin (7).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 1 , January 1963 , pp. 11 - 24
Copyright
Copyright © Cambridge Philosophical Society 1963

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)Arens, R. and Singer, I.Generalized analytic functions. Trans. American Math. Soc. 81 (1956), 379–393.CrossRefGoogle Scholar
(2)Beck, A., Corson, H. H. and Simon, A. B.The interior points of the product of two subsets of a locally compact group. Proc. American Math. Soc. 9 (1958), 648–652.CrossRefGoogle Scholar
(3)Hewitt, E. and Zuckerman, H. S.The l 1-algebra of a commutative semi-group. Trans. American Math. Soc. 83 (1956), 70–97.Google Scholar
(4)Loomis, L. H.An introduction to abstract harmonic analysis (Van Nostrand; New York, 1953).Google Scholar
(5)Naimark, M. A.Normed rings (Noordhoff; Groningen, 1959).Google Scholar
(6)Pontrjagin, L.Topological groups (Princeton, 1946).Google Scholar
(7)Rudin, W.Measure algebras on abelian groups. Bull. American Math. Soc. 65 (1959), 227–247.CrossRefGoogle Scholar
(8)Simon, A. B.Vanishing algebras. Trans. American Math. Soc. 92 (1959), 154–167.CrossRefGoogle Scholar
(9)Wang, J.-K.Multipliers of commutative Banach algebras. Pacific J. Math. 11 (1961), 1131–1149.CrossRefGoogle Scholar
(10)Wendel, J. G.Left centralizers and isomorphisms of group algebras. Pacific J. Math. 2 (1952), 251–261.CrossRefGoogle Scholar
(11)Wiener, N. and Pitt, H. R.On absolutely convergent Fourier-Stieltjes transforms. Duke Math. J. 4 (1938), 420–436.CrossRefGoogle Scholar
(12)Williamson, J. H.A theorem on algebras of measures on topological groups. Proc. Edinburgh Math. Soc. (2), 11 (1959), 195–206.CrossRefGoogle Scholar
(13)Williamson, J. H.The Wiener-Pitt phenomenon on the half-line. Proc. Edinburgh Math. Soc. (2), 13 (1962), 37–38.CrossRefGoogle Scholar