TY  - JOUR
A1  - Bandara, Lashi
A1  - McIntosh, Alan
A1  - Rosen, Andreas
T1  - Riesz continuity of the Atiyah
BT  - singer dirac operator under perturbations of the metric
JF  - Mathematische Annalen
N2  - We prove that the Atiyah–Singer Dirac operator in L2 depends Riesz continuously on L∞ perturbations of complete metrics g on a smooth manifold. The Lipschitz bound for the map depends on bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius. Our proof uses harmonic analysis techniques related to Calderón’s first commutator and the Kato square root problem. We also show perturbation results for more general functions of general Dirac-type operators on vector bundles.
Y1  - 2017
U6  - https://doi.org/10.1007/s00208-017-1610-7
SN  - 0025-5831
SN  - 1432-1807
VL  - 370
IS  - 1-2
SP  - 863
EP  - 915
PB  - Springer
CY  - Heidelberg
ER  - 
TY  - JOUR
A1  - Bandara, Menaka Lashitha
A1  - Rosen, Andreas
T1  - Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of local boundary conditions
JF  - Communications in partial differential equations
N2  - On a smooth complete Riemannian spin manifold with smooth compact boundary, we demonstrate that Atiyah-Singer Dirac operator in depends Riesz continuously on perturbations of local boundary conditions The Lipschitz bound for the map depends on Lipschitz smoothness and ellipticity of and bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius away from a compact neighbourhood of the boundary. More generally, we prove perturbation estimates for functional calculi of elliptic operators on manifolds with local boundary conditions.
KW  - Boundary value problems
KW  - Dirac operator
KW  - functional calculus
KW  - real-variable harmonic analysis
KW  - Riesz continuity
KW  - spectral flow
Y1  - 2019
U6  - https://doi.org/10.1080/03605302.2019.1611847
SN  - 0360-5302
SN  - 1532-4133
VL  - 44
IS  - 12
SP  - 1253
EP  - 1284
PB  - Taylor & Francis Group
CY  - Philadelphia
ER  - 
TY  - GEN
A1  - Bandara, Menaka Lashitha
A1  - Rosén, Andreas
T1  - Riesz continuity of the Atiyah–Singer Dirac operator under perturbations of local boundary conditions
T2  - Postprints der Universität Potsdam Mathematisch-Naturwissenschaftliche Reihe
N2  - On a smooth complete Riemannian spin manifold with smooth compact boundary, we demonstrate that Atiyah-Singer Dirac operator in depends Riesz continuously on perturbations of local boundary conditions The Lipschitz bound for the map depends on Lipschitz smoothness and ellipticity of and bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius away from a compact neighbourhood of the boundary. More generally, we prove perturbation estimates for functional calculi of elliptic operators on manifolds with local boundary conditions.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 758 
KW  - boundary value problems
KW  - Dirac operator
KW  - functional calculus
KW  - real-variable harmonic analysis
KW  - Riesz continuity
KW  - spectral flow
Y1  - 2019
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-434078
SN  - 1866-8372
IS  - 758
SP  - 1253
EP  - 1284
ER  -