### Abstract

For a closed codimension one submanifold Γ of a compact manifold M, let M_{Γ} be the manifold with boundary obtained by cutting M along Γ. Let A be an elliptic differential operator on M and B and C be two complementary boundary conditions on Γ. If (A, B) is an elliptic boundary valued problem on M_{Γ}, then one defines an elliptic pseudodifferential operator R of Neumann type on Γ and prove the following factorization formula for the ζ-regularized determinants: DetA Det(A, B) = KDetR, with K a local quantity depending only on the jets of the symbols of A, B and C along Γ. The particular case when M has dimension 2, A is the Laplace-Beltrami operator, and B resp. C is the Dirichlet resp. Neumann boundary condition is considered.

Original language | English (US) |
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Pages (from-to) | 34-65 |

Number of pages | 32 |

Journal | Journal of Functional Analysis |

Volume | 107 |

Issue number | 1 |

DOIs | |

State | Published - Jul 1992 |

### ASJC Scopus subject areas

- Analysis

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## Cite this

*Journal of Functional Analysis*,

*107*(1), 34-65. https://doi.org/10.1016/0022-1236(92)90099-5