Supplement to the paper “Quasianalytic perturbation of multi-parameter hyperbolic polynomials and symmetric matrices” (Ann. Polon. Math. 101 (2011), 275–291)

Krzysztof Jan Nowak¹

¹ Institute of Mathematics Jagiellonian University Łojasiewicza 6 30-348 Kraków, Poland

Annales Polonici Mathematici, Tome 103 (2012) no. 1, pp. 101-107.

Résumé

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 $\nu$-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, however, different methods and techniques. A recent paper by Parusiński–Rond validates Luengo's result, which allows us to resume our previous approach.

Détail

DOI : 10.4064/ap103-1-8

Mots-clés : imuj preprint investigated quasianalytic perturbation hyperbolic polynomials symmetric matrices applying quasianalytic version abhyankar jung theorem imuj preprint whose proof relied theorem luengo nu quasiordinary polynomials those papers ours suspended after had become aware luengos paper contained essential gap gave rise subsequent article quasianalytic perturbation theory which developed however different methods techniques recent paper parusi ski rond validates luengos result which allows resume previous approach