Determinants of zeroth order operators

Leonid Friedlander The University of Arizona Victor Guillemin Massachusetts Institute of Technology

Differential Geometry mathscidoc:1609.10046

Journal of Differential Geometry, 78, (1), 1-12, 2008
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.
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@inproceedings{leonid2008determinants,
  title={DETERMINANTS OF ZEROTH ORDER OPERATORS},
  author={Leonid Friedlander, and Victor Guillemin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909103048344927703},
  booktitle={Journal of Differential Geometry},
  volume={78},
  number={1},
  pages={1-12},
  year={2008},
}
Leonid Friedlander, and Victor Guillemin. DETERMINANTS OF ZEROTH ORDER OPERATORS. 2008. Vol. 78. In Journal of Differential Geometry. pp.1-12. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909103048344927703.
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