We study realizations of pseudodifferential operators acting on sections of vectorbundles 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 (A;H;D) for manifolds with boundary of arbitrary dimension, where 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 A in L(H) coincides with the continuous functions on the manifold being constant on each connected component of the boundary.
Boundary value problems with Atiyah-Patodi-Singer type conditions and spectral triples / Battisti, U.; Seiler, J.. - In: JOURNAL OF NONCOMMUTATIVE GEOMETRY. - ISSN 1661-6952. - STAMPA. - 11:3(2017), pp. 887-917.
|Titolo:||Boundary value problems with Atiyah-Patodi-Singer type conditions and spectral triples|
|Data di pubblicazione:||2017|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.4171/JNCG/11-3-4|
|Appare nelle tipologie:||1.1 Articolo in rivista|