Abstract
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.
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Axelsson, A., Keith, S. & McIntosh, A. Quadratic estimates and functional calculi of perturbed Dirac operators. Invent. math. 163, 455–497 (2006). https://doi.org/10.1007/s00222-005-0464-x
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DOI: https://doi.org/10.1007/s00222-005-0464-x