Radu Purice
Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania

We consider a real H\"ormander symbol of the type $S_{0,0}^0(\mathbb{R}^{d}\times \mathbb{R}^d)$, with a perturbation of the form $x\mapsto\,x+F(\delta \cdot x)$ with $F$ a smooth function with all its derivatives globally bounded, and $|\delta|\leq 1$. First, we prove that varying $\delta$ above $\delta=0$ the Hausdorff distance between the spectra is bounded by $\sqrt{|\delta|}$, and second, we show that the distance between the spectral edges is of order $|\delta|$. This work is done in collaboration with Horia Cornean (Aalborg University).