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Let $(M,g)$ be a compact smoothly stratified pseudomanifold with an iteratedcone-edge metric satisfying a spectral Witt condition. Under these assumptionsthe Hodge-Laplacian $\Delta$ is essentially self-adjoint. We establish theasymptotic expansion for the resolvent trace of $\Delta$. Our method proceedsby induction on the depth and applies in principle to a larger class ofsecond-order differential operators of regular-singular type, e.g., DiracLaplacians. Our arguments are functional analytic, do not rely on microlocaltechniques and are very explicit. The results of this paper provide a basis forstudying index theory and spectral invariants in the setting of smoothlystratified spaces and in particular allow for the definition ofzeta-determinants and analytic torsion in this general setup.

Resolvent Trace Asymptotics on Stratified Spaces