### Abstract

For an elliptic differential operator A over S^{1}, {Mathematical expression}, with A_{k}(x) in END(ℂ^{r}) and θ as a principal angle, the ζ-regularized determinant Det_{θ}A is computed in terms of the monodromy map P_{A}, associated to A and some invariant expressed in terms of A_{n} and A_{n-1}. A similar formula holds for finite difference operators. A number of applications and implications are given. In particular we present a formula for the signature of A when A is self adjoint and show that the determinant of A is the limit of a sequence of computable expressions involving determinants of difference approximation of A.

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

Pages (from-to) | 1-18 |

Number of pages | 18 |

Journal | Communications in Mathematical Physics |

Volume | 138 |

Issue number | 1 |

DOIs | |

State | Published - May 1991 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

^{1}.

*Communications in Mathematical Physics*,

*138*(1), 1-18. https://doi.org/10.1007/BF02099666

**On the determination of elliptic differential and finite difference operators in vector bundles over S ^{1}.** / Burghelea, D.; Friedlander, Leonid; Kappeler, T.

Research output: Contribution to journal › Article

^{1}',

*Communications in Mathematical Physics*, vol. 138, no. 1, pp. 1-18. https://doi.org/10.1007/BF02099666

^{1}. Communications in Mathematical Physics. 1991 May;138(1):1-18. https://doi.org/10.1007/BF02099666

}

TY - JOUR

T1 - On the determination of elliptic differential and finite difference operators in vector bundles over S1

AU - Burghelea, D.

AU - Friedlander, Leonid

AU - Kappeler, T.

PY - 1991/5

Y1 - 1991/5

N2 - For an elliptic differential operator A over S1, {Mathematical expression}, with Ak(x) in END(ℂr) and θ as a principal angle, the ζ-regularized determinant DetθA is computed in terms of the monodromy map PA, associated to A and some invariant expressed in terms of An and An-1. A similar formula holds for finite difference operators. A number of applications and implications are given. In particular we present a formula for the signature of A when A is self adjoint and show that the determinant of A is the limit of a sequence of computable expressions involving determinants of difference approximation of A.

AB - For an elliptic differential operator A over S1, {Mathematical expression}, with Ak(x) in END(ℂr) and θ as a principal angle, the ζ-regularized determinant DetθA is computed in terms of the monodromy map PA, associated to A and some invariant expressed in terms of An and An-1. A similar formula holds for finite difference operators. A number of applications and implications are given. In particular we present a formula for the signature of A when A is self adjoint and show that the determinant of A is the limit of a sequence of computable expressions involving determinants of difference approximation of A.

UR - http://www.scopus.com/inward/record.url?scp=0001304678&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001304678&partnerID=8YFLogxK

U2 - 10.1007/BF02099666

DO - 10.1007/BF02099666

M3 - Article

AN - SCOPUS:0001304678

VL - 138

SP - 1

EP - 18

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -