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A note on a result of K.D. Magill, Jr

Published online by Cambridge University Press:  17 April 2009

Eric Warren  and
S. Yamamuro
Eric Warren
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, B.C., Canada.
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Abstract

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The result of Magill concerning differentiable maps on the reals; namely, that all automorphisms of this semigroup are inner; is shown to be untrue in the case of analytic maps on the complexes. Also a characterization of the inner automorphisms of the analytic maps is given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 7 , Issue 2 , October 1972 , pp. 161 - 162
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Mackey, George W., Lectures on the theory of functions of a complex variable (Van Nostrand, Princeton, New Jersey; Toronto, Ontario; London; 1967).Google Scholar
[2]Magill, Kenneth D. Jr, “Automorphisms of the semigroup of all differentiable functions”, Glasgow Math. J. 8 (1967), 63–66.CrossRefGoogle Scholar
[3]Yamamuro, Sadayuki, “On the semigroup of differentiable mappings”, J. Austral. Math. Soc. 10 (1969), 503–510.CrossRefGoogle Scholar