SPECTRAL REGULARITY WITH RESPECT TO DILATIONS FOR A CLASS OF PSEUDO-DIFFERENTIAL OPERATORS.

CORNEAN, HORIA; PURICE, RADU

We continue the study of the perturbation problem discussed in H. D. Cornean and R. Purice (2023) and get rid of the "slow variation" assumption by considering symbols of the form a(x δ F(x), ξ) with α a real Hörmander symbol of class S 0,00(ℝd x ℝd) and F a smooth function with all its derivatives globally bounded, with |δ| ≤ 1. We prove that while the Hausdorff distance between the spectra of the Weyl quantization of the above symbols in a neighbourhood of δ = 0 is still of the order √|δ|, the distance between their spectral edges behaves like |δ|ν with ν ϵ [1/2,1) depending on the rate of decay of the second derivatives of F at infinity.

PSEUDODIFFERENTIAL operators; SINGULAR perturbations; SMOOTHNESS of functions; NEIGHBORHOODS; SIGNS & symbols

Romanian Journal of Pure & Applied Mathematics / Revue Roumaine de Mathematiques Pures et Appliquees, 2024, Vol 69, Issue 3/4, p445

0035-3965

Academic Journal

10.59277/RRMPA.2024.445.460