### Abstract

We express the ζ-regularized determinant of an elliptic pseudodifferential operator A over S^{1} with strongly invertible principal symbol in terms of the Fredholm determinant of an operator of determinant class, canonically associated to A, and local invariants. These invariants are given by explicit formulae involving the principal and subprincipal symbol of the operator. We remark that, generically, elliptic pseudodifferential operators have a strongly invertible principal symbol.

Original language | English (US) |
---|---|

Pages (from-to) | 496-513 |

Number of pages | 18 |

Journal | Integral Equations and Operator Theory |

Volume | 16 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1993 |

### Fingerprint

### Keywords

- MSC1991: Primary 34L05, Secondary 35S05

### ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory

### Cite this

^{1}

*Integral Equations and Operator Theory*,

*16*(4), 496-513. https://doi.org/10.1007/BF01205290

**Regularized determinants for pseudodifferential operators in vector bundles over S ^{1}
.** / Burghelea, D.; Friedlander, Leonid; Kappeler, T.

Research output: Contribution to journal › Article

^{1}',

*Integral Equations and Operator Theory*, vol. 16, no. 4, pp. 496-513. https://doi.org/10.1007/BF01205290

^{1}Integral Equations and Operator Theory. 1993 Dec;16(4):496-513. https://doi.org/10.1007/BF01205290

}

TY - JOUR

T1 - Regularized determinants for pseudodifferential operators in vector bundles over S1

AU - Burghelea, D.

AU - Friedlander, Leonid

AU - Kappeler, T.

PY - 1993/12

Y1 - 1993/12

N2 - We express the ζ-regularized determinant of an elliptic pseudodifferential operator A over S1 with strongly invertible principal symbol in terms of the Fredholm determinant of an operator of determinant class, canonically associated to A, and local invariants. These invariants are given by explicit formulae involving the principal and subprincipal symbol of the operator. We remark that, generically, elliptic pseudodifferential operators have a strongly invertible principal symbol.

AB - We express the ζ-regularized determinant of an elliptic pseudodifferential operator A over S1 with strongly invertible principal symbol in terms of the Fredholm determinant of an operator of determinant class, canonically associated to A, and local invariants. These invariants are given by explicit formulae involving the principal and subprincipal symbol of the operator. We remark that, generically, elliptic pseudodifferential operators have a strongly invertible principal symbol.

KW - MSC1991: Primary 34L05, Secondary 35S05

UR - http://www.scopus.com/inward/record.url?scp=0040483180&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040483180&partnerID=8YFLogxK

U2 - 10.1007/BF01205290

DO - 10.1007/BF01205290

M3 - Article

VL - 16

SP - 496

EP - 513

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 4

ER -