Quadratic estimates and functional calculi of perturbed Dirac operators

被引：81

作者：

Axelsson, A ^{[1
]}

Keith, S ^{[1
]}

McIntosh, A ^{[1
]}

机构：

[1] Australian Natl Univ, Ctr Math & Its Applicat, Canberra, ACT 0200, Australia

来源：

INVENTIONES MATHEMATICAE | 2006年 / 163卷 / 03期

关键词：

D O I：

10.1007/s00222-005-0464-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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-infinity changes in the metric. We also recover a unified proof of many results in the Calderon program, including the Kato square root problem and the boundedness of the Cauchy operator on Lipschitz curves and surfaces.

引用

页码：455 / 497

页数：43

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