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EnglishWe study realizations of pseudodifferential operators acting on sections of vector-bundles on a smooth, compact manifold with boundary, subject to conditions of Atiyah-Patodi-Singer type. Ellipticity and Fredholm property, compositions, adjoints and self-adjointness of such realizations are discussed. We construct regular spectral triples $(\mathcal{A},\mathcal{H},\mathcal{D})$ for manifolds with boundary of arbitrary dimension, where $\mathcal{H}$ is the space of square integrable sections. Starting out from Dirac operators with APS-conditions, these triples are even in case of even dimensional manifolds; we show that the closure of $\mathcal{A}$ in $\mathscr{L}(\mathcal{H})$ coincides with the continuous functions on the manifold being constant on each connected component of the boundary.
| Titolo: | Boundary value problems with Atiyah-Patodi-Singer type conditions and spectral triples |
| Autori Riconosciuti: | |
| Autori: | Battisti, U.; Seiler, J. |
| Data di pubblicazione: | 2017 |
| Abstract: | We study realizations of pseudodifferential operators acting on sections of vector-bundles on a smooth, compact manifold with boundary, subject to conditions of Atiyah-Patodi-Singer type. Ellipticity and Fredholm property, compositions, adjoints and self-adjointness of such realizations are discussed. We construct regular spectral triples $(\mathcal{A},\mathcal{H},\mathcal{D})$ for manifolds with boundary of arbitrary dimension, where $\mathcal{H}$ is the space of square integrable sections. Starting out from Dirac operators with APS-conditions, these triples are even in case of even dimensional manifolds; we show that the closure of $\mathcal{A}$ in $\mathscr{L}(\mathcal{H})$ coincides with the continuous functions on the manifold being constant on each connected component of the boundary. |
| Volume: | 11 |
| Fascicolo: | 3 |
| Pagina iniziale: | 887 |
| Pagina finale: | 917 |
| Digital Object Identifier (DOI): | 10.4171/JNCG/11-3-4 |
| URL: | https://arxiv.org/abs/1503.02897 |
| Parole Chiave: | Spectral triples, manifolds with boundary, boundary value problems with APS-type conditions, pseudodifferential operators |
| Rivista: | JOURNAL OF NONCOMMUTATIVE GEOMETRY |
| Appare nelle tipologie: | 03A-Articolo su Rivista |
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