### 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) |
---|---|

Pages (from-to) | 34-65 |

Number of pages | 32 |

Journal | Journal of Functional Analysis |

Volume | 107 |

Issue number | 1 |

DOIs | |

State | Published - 1992 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Analysis

### Cite this

*Journal of Functional Analysis*,

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

**Meyer-vietoris type formula for determinants of elliptic differential operators.** / Burghelea, D.; Friedlander, Leonid; Kappeler, T.

Research output: Contribution to journal › Article

*Journal of Functional Analysis*, vol. 107, no. 1, pp. 34-65. https://doi.org/10.1016/0022-1236(92)90099-5

}

TY - JOUR

T1 - Meyer-vietoris type formula for determinants of elliptic differential operators

AU - Burghelea, D.

AU - Friedlander, Leonid

AU - Kappeler, T.

PY - 1992

Y1 - 1992

N2 - For a closed codimension one submanifold Γ of a compact manifold M, let MΓ 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 MΓ, 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.

AB - For a closed codimension one submanifold Γ of a compact manifold M, let MΓ 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 MΓ, 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.

UR - http://www.scopus.com/inward/record.url?scp=0002427838&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002427838&partnerID=8YFLogxK

U2 - 10.1016/0022-1236(92)90099-5

DO - 10.1016/0022-1236(92)90099-5

M3 - Article

VL - 107

SP - 34

EP - 65

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 1

ER -