On Multiplicative Properties of Determinants

2018/01/31 by Friedlander, Leonid
#58J52 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1801.10606

Abstract

Let A be an elliptic pseudodifferential operator of positive order on a compact closed manifold, and let T be a pseudodifferential operator of negative order such that T^m is of trace class. We compute logdet(A(I+T))-logdet A-logdet_m (I+T) where first two determinants are zeta function regularized, and the last one is a regularized Fredholm determinant.

Related

• Determinants of elliptic pseudo-differential operators
• Geometry of determinants of elliptic operators
• Zeta and Fredholm determinants of self-adjoint operators
• The Residue Determinant
• A resolvent approach to traces and zeta Laurent expansions