Resolvent trace asymptotics on stratified spaces

Autor:	Luiz Hartmann, Boris Vertman, Matthias Lesch
Rok vydání:	2021
Předmět:	Pure mathematics Trace (linear algebra) Basis (linear algebra) Ocean Engineering Type (model theory) Differential operator Mathematics - Spectral Theory Iterated function FOS: Mathematics 35J75 58J35 Analytic torsion Asymptotic expansion Spectral Theory (math.SP) Mathematics Resolvent
Zdroj:	Pure and Applied Analysis. 3:75-108
ISSN:	2578-5885 2578-5893
DOI:	10.2140/paa.2021.3.75
Popis:	Let $(M,g)$ be a compact smoothly stratified pseudomanifold with an iterated cone-edge metric satisfying a spectral Witt condition. Under these assumptions the Hodge-Laplacian $\Delta$ is essentially self-adjoint. We establish the asymptotic expansion for the resolvent trace of $\Delta$. Our method proceeds by induction on the depth and applies in principle to a larger class of second-order differential operators of regular-singular type, e.g., Dirac Laplacians. Our arguments are functional analytic, do not rely on microlocal techniques and are very explicit. The results of this paper provide a basis for studying index theory and spectral invariants in the setting of smoothly stratified spaces and in particular allow for the definition of zeta-determinants and analytic torsion in this general setup.
Databáze:	OpenAIRE
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