We establish new Lipschitz-type bounds for functions of operators with noncompact perturbations that produce Schatten class resolvent differences. The results apply to suitable perturbations of Dirac and Schrödinger operators, including some long-range and random potentials, and to important classes of test functions. The key feature of these bounds is an explicit dependence on the Lipschitz seminorm and decay parameters of the respective scalar functions and, in the case of Dirac and Schrödinger operators, on the L^p- or ℓ^p(L²)-norm of the potential.

中文翻译：

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Lipschitz估计Dirac和Schrödinger算子的功能

我们为产生Schatten类可分辨差异的非紧凑扰动的算子函数建立新的Lipschitz型边界。结果适用于Dirac和Schrödinger算符的适当扰动，包括一些远程和随机势，并且适用于重要的测试函数类别。这些界限中的关键特征是在李普希茨半范和各自的标量函数衰减参数，并且在狄拉克和薛定谔运营商的情况下的显式依赖性，在大号^p -或ℓ ^p（大号²范数的电势的） 。