Formal relations between quasianalytic functions of some fixed class

F. Broglia, A. Elkhadiri, and F. Pieroni. "Formal relations between quasianalytic functions of some fixed class." Annales Polonici Mathematici 83.1 (2004): 35-40. <http://eudml.org/doc/280227>.

@article{F2004,
abstract = {In [Ga] Gabrielov has given conditions under which the completion of the kernel of a morphism φ: A → B between analytic rings coincides with the kernel of the induced morphism φ̂: Â → B̂ between the completions. If B is a domain, a sufficient condition is that rk φ = dim(Â/ker φ̂), where rk φ is the rank of the jacobian matrix of φ considered as a matrix over the quotient field of B. We prove that the above property holds in a fixed quasianalytic Denjoy-Carleman class if and only if the class coincides with the ring of germs of analytic functions.},
author = {F. Broglia, A. Elkhadiri, F. Pieroni},
journal = {Annales Polonici Mathematici},
keywords = {Denjoy-Carleman class; Gabrielov property; quasianalytic functions},
language = {eng},
number = {1},
pages = {35-40},
title = {Formal relations between quasianalytic functions of some fixed class},
url = {http://eudml.org/doc/280227},
volume = {83},
year = {2004},
}

TY - JOUR
AU - F. Broglia
AU - A. Elkhadiri
AU - F. Pieroni
TI - Formal relations between quasianalytic functions of some fixed class
JO - Annales Polonici Mathematici
PY - 2004
VL - 83
IS - 1
SP - 35
EP - 40
AB - In [Ga] Gabrielov has given conditions under which the completion of the kernel of a morphism φ: A → B between analytic rings coincides with the kernel of the induced morphism φ̂: Â → B̂ between the completions. If B is a domain, a sufficient condition is that rk φ = dim(Â/ker φ̂), where rk φ is the rank of the jacobian matrix of φ considered as a matrix over the quotient field of B. We prove that the above property holds in a fixed quasianalytic Denjoy-Carleman class if and only if the class coincides with the ring of germs of analytic functions.
LA - eng
KW - Denjoy-Carleman class; Gabrielov property; quasianalytic functions
UR - http://eudml.org/doc/280227
ER -