For a class of pseudodifferential operators, the distance between spectral edges under a dilation-type perturbation decays like |δ|^ν with ν between 1/2 and 1, depending on the decay rate of the second derivatives of the perturbation field.
H¨ ormander: The Analysis of Linear Partial Differential Operators III: Ps eudo-Differential Operators
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Spectral regularity with respect to dilations for a class of pseudodifferential operators
For a class of pseudodifferential operators, the distance between spectral edges under a dilation-type perturbation decays like |δ|^ν with ν between 1/2 and 1, depending on the decay rate of the second derivatives of the perturbation field.