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

Krzysztof Jan Nowak. "Supplement to the paper "Quasianalytic perturbation of multi-parameter hyperbolic polynomials and symmetric matrices" (Ann. Polon. Math. 101 (2011), 275-291)." Annales Polonici Mathematici 103.1 (2012): 101-107. <http://eudml.org/doc/280743>.

@article{KrzysztofJanNowak2012,
abstract = {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, however, different methods and techniques. A recent paper by Parusiński-Rond validates Luengo's result, which allows us to resume our previous approach.},
author = {Krzysztof Jan Nowak},
journal = {Annales Polonici Mathematici},
keywords = {quasianalytic perturbation; hyperbolic polynomials; quasianalytic and arc-quasianalytic functions; polynomially bounded structures; eigenvalues; eigenspaces; symmetric and antisymmetric matrices; spectral theorem; quasianalytic diagonalization},
language = {eng},
number = {1},
pages = {101-107},
title = {Supplement to the paper "Quasianalytic perturbation of multi-parameter hyperbolic polynomials and symmetric matrices" (Ann. Polon. Math. 101 (2011), 275-291)},
url = {http://eudml.org/doc/280743},
volume = {103},
year = {2012},
}

TY - JOUR
AU - Krzysztof Jan Nowak
TI - Supplement to the paper "Quasianalytic perturbation of multi-parameter hyperbolic polynomials and symmetric matrices" (Ann. Polon. Math. 101 (2011), 275-291)
JO - Annales Polonici Mathematici
PY - 2012
VL - 103
IS - 1
SP - 101
EP - 107
AB - 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, however, different methods and techniques. A recent paper by Parusiński-Rond validates Luengo's result, which allows us to resume our previous approach.
LA - eng
KW - quasianalytic perturbation; hyperbolic polynomials; quasianalytic and arc-quasianalytic functions; polynomially bounded structures; eigenvalues; eigenspaces; symmetric and antisymmetric matrices; spectral theorem; quasianalytic diagonalization
UR - http://eudml.org/doc/280743
ER -