Multiparameter resolvent trace expansion for elliptic boundary problems

TL;DR

This paper develops a detailed multiparameter resolvent trace expansion framework for elliptic boundary problems, enhancing understanding of spectral properties and zeta-determinants on revolution surfaces.

Contribution

It introduces a novel multiparameter resolvent trace expansion approach for elliptic boundary value problems, with applications to zeta-determinants on revolution surfaces.

Findings

Established multiparameter resolvent trace expansions for elliptic boundary problems.

Applied the framework to regularized sums of zeta-determinants.

Extended analysis to revolution surfaces with polyhomogeneous properties.

Abstract

We establish multiparameter resolvent trace expansions for elliptic boundary value problems, polyhomogeneous both in the resolvent and the auxiliary parameter. The present analysis is rooted in the joint project with Matthias Lesch on multiparameter resolvent trace expansions on revolution surfaces with applications to regularized sums of zeta-determinants.