Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-22T06:50:38.806Z Has data issue: false hasContentIssue false
  • English
  • Français

An elementary proof of part of a classical conjecture

Published online by Cambridge University Press:  17 April 2009

R. J. Gaudet  and
J. L. B. Gamlen
R. J. Gaudet
Affiliation:
The University of Alberta, Edmonton, Canada.
J. L. B. Gamlen
Affiliation:
The University of Alberta, Edmonton, Canada.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An elementary proof is given for the Lp conjecture, p > 2, which states that for a locally compact group G, Lp (G) (p > 2) is closed under convolution if and only if G is compact.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 3 , Issue 3 , December 1970 , pp. 289 - 292
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Hewitt, Edwin; Ross, Kenneth A., Abstract harmonic analysis. Vol. I. (Die Grundlehren der mathematischen Wissenschaften, Band 115, Academic Press, New York; Springer-Verlag, Berlin, Göttingen, Heidelberg, 1963).Google Scholar
[2]Leptin, Horst, “Faltungen von Borelschen Massen mit Lp-Funktionen auf lokal kompakten Gruppen”, Math. Ann. 163 (1966), 111–117.CrossRefGoogle Scholar
[3]Leptin, Horst, “On a certain invariant of a locally compact group”, Bull. Amer. Math. Soc. 72 (1966), 870–874.CrossRefGoogle Scholar
[4]Rajagopalan, M., “On the Lp-space of a locally compact group”, Colloq. Math. 10 (1963), 49–52.CrossRefGoogle Scholar
[5]Rajagopalan, M., “Lp -conjecture for locally compact groups. I”, Trans. Amer. Math. Soc. 125 (1966), 216–222.Google Scholar
[6]Rajagopalan, M. and Zelazko, W., “Lp-conjecture for solvable locally compact groups”, J. Indian Math. Soc. (N.S.) 29 (1965), 87–92.Google Scholar
[7]Zelazko, W., “On the algebras Lp of locally compact groups”, Colloq. Math. 8 (1961), 115–120.CrossRefGoogle Scholar
[8]Zelazko, W., “A note on Lp -algebras”, Colloq. Math. 10 (1963), 53–56.CrossRefGoogle Scholar