The Residue Determinant

Details The Residue Determinant The Residue Determinant

2004-06-14

arxiv.org/abs/math/0406268v7

Mathematics

Analysis of PDEs

Scientific paper

The purpose of this paper is to present the construction of a canonical determinant functional on elliptic pseudodifferential operators associated to the Guillemin-Wodzicki residue trace. The resulting functional is multiplicative, a local invariant, and not defined by a regularization procedure. The residue determinant is consequently a quite different object to the zeta function (quasi-) determinant, which is non-local and non-multiplicative.

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