The BFK-gluing formula for zeta-determinants and the conformal rescaling of a metric
In this article, the authors use the property that the homogeneous symbols of the Dirichlet-to-Neumann operator are invariants with respect to conformal rescaling of Riemannian metrics and the result in [\textit{K. Kirsten} and \textit{Y. Lee}, J. Math. Phys. 56, No. 12, 123501, 19 p. (2015; Zbl 1334.58022)] (where the authors studied BFK-gluing formula on a warped product manifold) to recover the main result of [\textit{K. Kirsten} et. al., J. Spectr. Theory. 10, 1007--1051 (2020; Zbl 1476.58034)]. The authors also prove a relation about the value at zero of the zeta function associated to the Dirchlet-to-Neumann operator; this result was obtained in [\textit{K. Kirsten} et. al., J. Geom. Anal. 28, 3856--3891 (2018; Zbl 1409.58015)] on a warped product manifold. This article is a chapter of the book [\textit{F. Gesztesy} (ed.) and \textit{A. Martinez-Finkelshtein} (ed.), From operator theory to orthogonal polynomials, combinatorics, and number theory. A~volume in honor of Lance Littlejohn's 70th birthday. Cham: Birkhäuser (2021; Zbl 1479.47003)]. For the entire collection see [Zbl 1479.47003].
scientific article; zbMATH DE number 7456832
scientific article