Continuity of Weighted Dirac Spectra

TL;DR

This paper proves the continuous dependence of weighted Dirac spectra on weights and provides Lipschitz estimates for spectrum variation under smooth weight changes.

Contribution

It establishes the spectral continuity for weighted Dirac operators and derives quantitative Lipschitz bounds using a variational identity.

Findings

Weighted Dirac spectra depend continuously on weights within elliptic classes.

Lipschitz estimates for spectrum variation are obtained for differentiable weight families.

The results are based on a weighted Hellmann–Feynman variational identity.

Abstract

For the weighted Dirac eigenvalue problem, we show that the two-sided weighted spectrum depends continuously on the weight under continuous deformations within a uniformly elliptic class. Moreover, for differentiable families of weights we obtain a quantitative Lipschitz estimate for the full spectrum in the arsinh--metric, based on a weighted Hellmann--Feynman variational identity.