Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T13:26:25.071Z Has data issue: false hasContentIssue false
  • English
  • Français

On C0-Sufficiency of Complex Jets

Published online by Cambridge University Press:  20 November 2018

S. H. Chang  and
Y. C. Lu
S. H. Chang
Affiliation:
Pennsylvania State University, University Park, Pennsylvania
Y. C. Lu
Affiliation:
Ohio State University, Columbus, Ohio
Rights & Permissions [Opens in a new window]

Extract

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.

In this paper we shall study the sufficiency of complex jets. Let A (Cn, C) be the set of all analytic functions f : Cn → C with f (0) = 0. We call two functions f and g of A (Cn, C) equivalent of order r at 0 if, at 0, their Taylor expansions up to and including the terms of degree ≦ r are identical.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 4 , August 1973 , pp. 874 - 880
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Hartman, P., Ordinary differential equations (Wiley, New York, 1964).Google Scholar
2. Kuiper, N. H., C1-equivalence of functions near isolated critical points, Symposium Infinite Dimensional Topology, Annals of Math. Studies, No. 69, 1972.Google Scholar
3. Kuo, T. C., On C°-sufficiency of jets of potential functions, Topology 8 (1969), 167–171.Google Scholar
4. Kuo, T. C., A complete determination of C°-sufficiency in Jr(2, 1), Invent. Math. 8 (1969), 226–235.Google Scholar
5. Lu, Y. C., Sufficiency of jets in Jr(2, 1) via decomposition, Invent. Math. 10 (1970), 119–127.Google Scholar
6. Mather, J. N., Stability of C∞ mappings. Ill: finitely determined map-germs, Publ. Math. I. H. E. S. 35 (1968), 127–156.Google Scholar