Determinants of zeroth order operators

Friedlander, Leonid; Guillemin, Victor

J. Differential Geom., Tome 78 (2008) no. 1, p. 1-12 / Harvested from Project Euclid

Résumé

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.

Publié le : 2008-01-15
Classification:

@article{1197320601,
     author = {Friedlander, Leonid and Guillemin, Victor},
     title = {Determinants of zeroth order operators},
     journal = {J. Differential Geom.},
     volume = {78},
     number = {1},
     year = {2008},
     pages = { 1-12},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1197320601}
}

Friedlander, Leonid; Guillemin, Victor. Determinants of zeroth order operators. J. Differential Geom., Tome 78 (2008) no. 1, pp.  1-12. http://gdmltest.u-ga.fr/item/1197320601/