Hostname: page-component-74656f9884-rdgjk Total loading time: 0 Render date: 2026-11-09T14:08:35.147Z Has data issue: false hasContentIssue false
  • English
  • Français

Functional Dependence and Analytic Functions

Published online by Cambridge University Press:  20 November 2018

P. Ramankutty
P. Ramankutty*
Affiliation:
Department of Mathematics, University of Auckland, Auckland, New Zealand
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.

Without appealing to the Cauchy theorem or its corollaries, it is proved that the real and imaginary parts of a non-constant complex-valued analytic function of several complex variables are functionally independent. This unifies and generalizes some results sporadically treated in standard treatises on function theory.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 3 , 01 September 1979 , pp. 367 - 369
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Ahlfors, L. V., Complex Analysis, 2nd Edition, McGraw-Hill, New York, 1966. MR 32 #5844.Google Scholar
2. Burkill, J. C. and Burkill, H. Second Course in Mathematical Analysis, Cambridge Univ. Press, 1970. MR 41 #3197.Google Scholar
3. Churchill, R. V., Brown, J. W. and Verhey, R. F., Complex Variables and Applications, 3rd Edition, McGraw-Hill, New York, 1974. MR 22 #3793 and MR 50 #580.Google Scholar
4. Conway, J. B., Functions of One Complex Variable, Springer-Verlag, New York, 1973.Google Scholar
5. Heins, M., Complex Function Theory, Academic Press, New York, 1968. MR 39 #413.Google Scholar