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Quadratic estimates and functional calculi of perturbed Dirac operators

Axelsson, Andreas; Keith, Stephen; McIntosh, Alan


We prove quadratic estimates for complex perturbations of Dirac-type operators, and thereby show that such operators have a bounded functional calculus. As an application we show that spectral projections of the Hodge-Dirac operator on compact manifolds depend analytically on L ∞ changes in the metric. We also recover a unified proof of many results in the Calderón program, including the Kato square root problem and the boundedness of the Cauchy operator on Lipschitz curves and surfaces.

CollectionsANU Research Publications
Date published: 2006
Type: Journal article
Source: Inventiones Mathematicae
DOI: 10.1007/s00222-005-0464-x


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