Spectral regularity with respect to dilations for a class of pseudodifferential operators

Horia Cornean, Radu Purice

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Abstract

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 a a real Hörmander symbol of class S00,0(Rd ×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 ∈ [1/2, 1) depending on the rate of decay of the second derivatives of F at infinity.

OriginalsprogEngelsk
TidsskriftRevue Roumaine de Mathematiques Pures et Appliquees
Vol/bind69
Udgave nummer3-4
Sider (fra-til)445-460
Antal sider16
ISSN0035-3965
DOI
StatusUdgivet - 2024

Bibliografisk note

Publisher Copyright:
© 2024, Publishing House of the Romanian Academy. All rights reserved.

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