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Journal of Spectral Theory


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Volume 8, Issue 4, 2018, pp. 1295–1348
DOI: 10.4171/JST/228

Published online: 2018-07-25

On the domain of Dirac and Laplace type operators on stratified spaces

Luiz Hartmann[1], Matthias Lesch[2] and Boris Vertman[3]

(1) Universidade Federal de São Carlos, Brazil
(2) Universität Bonn, Germany
(3) Universität Oldenburg, Germany

We consider a generalized Dirac operator on a compact stratified space with an iterated cone-edge metric. Assuming a spectral Witt condition, we prove its essential self-adjointness and identify its domain and the domain of its square with weighted edge Sobolev spaces. This sharpens previous results where the minimal domain is shown only to be a subset of an intersection of weighted edge Sobolev spaces. Our argument does not rely on microlocal techniques and is very explicit. The novelty of our approach is the use of an abstract functional analytic notion of interpolation scales. Our results hold for the Gauss–Bonnet and spin Dirac operators satisfying a spectral Witt condition.

Keywords: Stratified spaces, iterated cone-edge metrics, minimal domain

Hartmann Luiz, Lesch Matthias, Vertman Boris: On the domain of Dirac and Laplace type operators on stratified spaces. J. Spectr. Theory 8 (2018), 1295-1348. doi: 10.4171/JST/228