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Examples in the theory of sufficiency of jets. (English) Zbl 0594.58008
Summary: It is shown that for a given nonnegative integer s, there exist a positive integer r(s) and an r(s)-jet $$v_ s$$ with source at $$O\in {\mathbb{R}}^ 3$$ 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 $$O\in {\mathbb{C}}^ 2$$ which is V-sufficient but not $$C^ 0$$-sufficient in the class of holomorphic realizations is constructed.

##### MSC:
 58A20 Jets in global analysis 57R45 Singularities of differentiable mappings in differential topology
##### Keywords:
jet; jet with source; holomorphic realizations
Full Text:
##### References:
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