Hostname: page-component-84b7d79bbc-tsvsl Total loading time: 0 Render date: 2024-07-28T04:41:31.081Z Has data issue: false hasContentIssue false

On certain function spaces and group structures

Published online by Cambridge University Press:  17 April 2009

Hiroshi Yamaguchi
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo, Japan.
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.

We generalize a result of Walter Rudin about the structure of a compact abelian group G for which C(G) + H(G) is a closed subalgebra of L(G).

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Boas, Ralph Philip Jr, Entire functions (Pure and Applied Mathematics, 5. Academic Press, New York, 1954).Google Scholar
[2]Hewitt, Edwin, Ross, Kenneth A., Abstract harmonic analysis, Volume II (Die Grundlehren der mathematischen Wissenschaften, 152. Springer-Verlag, Berlin, Heidelberg, New York, 1970).Google Scholar
[3]Rudin, Walter, Fourier analysis on groups (interscience Tracts in Pure and Applied Mathematics, 12. Interscience [John Wiley & Sons], New York, London, 1962).Google Scholar
[4]Rudin, Walter, “Spaces of type H + C”, Ann. Inst. Fourier (Grenoble) 25 (1975), 99125.Google Scholar
[5]Sarason, Donald, “Algebras of functions on the unit circle”, Bull. Amer. Math. Soc. 79 (1973), 286299.CrossRefGoogle Scholar
[6]Sarason, Donald, “Functions of vanishing mean oscillation”, Trans. Amer. Math. Soc. 207 (1975), 391405.Google Scholar