## Abstract

In this paper we study the question of the existence of a continuous inverse to the multiplication mapping (formula presented) defined on pairs of C00 functions on a manifold M. Obviously, restrictions must be imposed on the domain of such an inverse. This leads us to the study of a modified problem: Find an appropriate domain for the inverse of (formula presented) mapping of the manifold M into an analytic manifold N and p is a fixed analytic function on N. We prove a theorem adequate for application to the study of inverting the mapping (formula presented), where A is a vector valued C function and A is a square matrix valued C00 function on M whose determinant may vanish on a nowhere dense set.

Original language | English |
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Pages (from-to) | 573-583 |

Number of pages | 11 |

Journal | Transactions of the American Mathematical Society |

Volume | 292 |

Issue number | 2 |

DOIs | |

State | Published - Dec 1985 |

Externally published | Yes |

## Keywords

- Continuity of division
- Continuous dependence of solutions on parameters
- Division of distributions
- Division of smooth functions
- Function spaces
- Mather Division Theorem
- Matrix equations