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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Examples in the theory of sufficiency of jets


Author: Wojciech Kucharz
Journal: Proc. Amer. Math. Soc. 96 (1986), 163-166
MSC: Primary 58C27; Secondary 57R45
MathSciNet review: 813830
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Abstract: It is shown that for a given nonnegative integer $ s$, there exist a positive integer $ r(s)$ and an $ r(s)$-jet $ {\upsilon _s}$ with source at $ O \in {{\mathbf{R}}^3}$ which is not $ V$-sufficient in the class of $ {C^{r(s) + s}}$-realizations and is $ {C^0}$-sufficient in the class of $ {C^{r(s) + s + 1}}$-realizations. In the complex case, a jet with source at $ O \in {{\mathbf{C}}^2}$ which is $ V$-sufficient but not $ {C^0}$-sufficient in the class of holomorphic realizations is constructed.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0813830-1
PII: S 0002-9939(1986)0813830-1
Article copyright: © Copyright 1986 American Mathematical Society