Stability and stabilizability for means.
In IMUJ Preprint 2009/05 we investigated the quasianalytic perturbation of hyperbolic polynomials and symmetric matrices by applying our quasianalytic version of the Abhyankar-Jung theorem from IMUJ Preprint 2009/02, whose proof relied on a theorem by Luengo on ν-quasiordinary polynomials. But those papers of ours were suspended after we had become aware that Luengo's paper contained an essential gap. This gave rise to our subsequent article on quasianalytic perturbation theory, which developed,...
We generalize to some classes of ultradifferentiable jets or functions the classical Łojasiewicz Division Theorem and Glaeser Composition Theorem. The proof uses the desingularization results by Hironaka, Bierstone and Milman.
We prove a Weierstrass division formula for Whitney jets ∂̅-flat on arbitrary compact subsets of the complex plane. We also give results for Carleman classes.