## Abstract

We prove two theorems of N. Kuiper by standard methods of the calculus on Banach spaces. C^{0}-sufficiency for C^{r}-functions of the r-jet of a real valued C^{r}-function of lowest degree r_{0} ≥ 2 on a Hilbert space follows from Kuiper's condition Q(r) also on a Banach space endowed with smooth partitions of unity. A new proof is given of the C^{1}-sufficiency for C^{r + p}-functions, p ≥ r - r_{0}, of the r + p-jet of a Q(r)-function on Hilbert space that also holds on Banach space modulo a further condition on the behavior of the function near its degenerate critical point.

Original language | English (US) |
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Pages (from-to) | 331-337 |

Number of pages | 7 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 32 |

Issue number | 2 |

DOIs | |

State | Published - Nov 1970 |

Externally published | Yes |

## ASJC Scopus subject areas

- Analysis
- Applied Mathematics

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