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. [10.4171/JNCG/11-3-4]

Boundary value problems with Atiyah-Patodi-Singer type conditions and spectral triples

Battisti U.;
2017

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11583/2839319