Sharp spectral stability for a class of singularly perturbed pseudo-differential operators

  • Horia D. Cornean

    Aalborg Universitet, Denmark
  • Radu Purice

    “Simion Stoilow” Institute of Mathematics of the Romanian Academy, Bucharest, Romania
Sharp spectral stability for a class of singularly perturbed pseudo-differential operators cover
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Abstract

Let be a real Hörmander symbol of the type , let be a smooth function with all its derivatives globally bounded, and let be the self-adjoint Weyl quantization of the perturbed symbols , where . First, we prove that the Hausdorff distance between the spectra of and is bounded by , and we give examples where spectral gaps of this magnitude can open when . Second, we show that the distance between the spectral edges of and (and also the edges of the inner spectral gaps, as long as they remain open at ) are of order , and give a precise dependence on the width of the spectral gaps.

Cite this article

Horia D. Cornean, Radu Purice, Sharp spectral stability for a class of singularly perturbed pseudo-differential operators. J. Spectr. Theory 13 (2023), no. 3, pp. 1129–1144

DOI 10.4171/JST/471