Quadratic estimates and functional calculi of perturbed Dirac operators
Quadratic estimates and functional calculi of perturbed Dirac operators
复制标题
扰动狄拉克算子的二次估计和泛函计算
DOI：
10.1007/s00222-005-0464-x
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发表时间：
2004
影响因子：
3.1
通讯作者：
A. Mcintosh
中科院分区：
文献类型：
--
作者：
A. Axelsson;S. Keith;A. Mcintosh
我们证明了dirac型算子的复扰动的二次估计，从而证明了这类算子具有有界泛函演算。作为一个应用，我们证明了紧流形上Hodge-Dirac算子的谱投影解析地依赖于度规的L∞变化。我们还恢复了Calderón程序中许多结果的统一证明，包括加藤平方根问题和Lipschitz曲线和面上Cauchy算子的有界性。
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.