### Abstract

For compact Riemannian manifolds all of whose geodesics are closed (aka Zoll manifolds) one can define the determinant of a zeroth order pseudodifferential operator by mimicking Szego's definition of this determinant for the operator: multiplication by a bounded function, on the Hilbert space of square-integrable functions on the circle. In this paper we prove that the non-local contribution to this determinant can be computed in terms of a much simpler "zeta-regularized" determinant.

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

Pages (from-to) | 1-12 |

Number of pages | 12 |

Journal | Journal of Differential Geometry |

Volume | 78 |

Issue number | 1 |

State | Published - Jan 2008 |

### Fingerprint

### ASJC Scopus subject areas

- Algebra and Number Theory
- Analysis
- Geometry and Topology

### Cite this

*Journal of Differential Geometry*,

*78*(1), 1-12.

**Determinants of zeroth order operators.** / Friedlander, Leonid; Guillemin, Victor.

Research output: Contribution to journal › Article

*Journal of Differential Geometry*, vol. 78, no. 1, pp. 1-12.

}

TY - JOUR

T1 - Determinants of zeroth order operators

AU - Friedlander, Leonid

AU - Guillemin, Victor

PY - 2008/1

Y1 - 2008/1

N2 - For compact Riemannian manifolds all of whose geodesics are closed (aka Zoll manifolds) one can define the determinant of a zeroth order pseudodifferential operator by mimicking Szego's definition of this determinant for the operator: multiplication by a bounded function, on the Hilbert space of square-integrable functions on the circle. In this paper we prove that the non-local contribution to this determinant can be computed in terms of a much simpler "zeta-regularized" determinant.

AB - For compact Riemannian manifolds all of whose geodesics are closed (aka Zoll manifolds) one can define the determinant of a zeroth order pseudodifferential operator by mimicking Szego's definition of this determinant for the operator: multiplication by a bounded function, on the Hilbert space of square-integrable functions on the circle. In this paper we prove that the non-local contribution to this determinant can be computed in terms of a much simpler "zeta-regularized" determinant.

UR - http://www.scopus.com/inward/record.url?scp=39749188220&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=39749188220&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:39749188220

VL - 78

SP - 1

EP - 12

JO - Journal of Differential Geometry

JF - Journal of Differential Geometry

SN - 0022-040X

IS - 1

ER -