Preparation theorems for matrix valued functions

@article{Dencker1993,
abstract = {We generalize the Malgrange preparation theorem to matrix valued functions $F(t,x)\in C^\infty (\{\bf R\}\times \{\bf R\}^n)$ satisfying the condition that $t\mapsto \, \{\rm det\}\, F(t,0)$ vanishes to finite order at $t=0$. Then we can factor $F(t,x) = C(t,x)P(t,x)$ near (0,0), where $C(t,x)\in C^\infty $ is inversible and $P(t,x)$ is polynomial function of $t$ depending $C^\infty $ on $x$. The preparation is (essentially) unique, up to functions vanishing to infinite order at $x=0$, if we impose some additional conditions on $P(t,x)$. We also have a generalization of the division theorem, and analytic versions generalizing the Weierstrass preparation and division theorems.},
author = {Dencker, Nils},
journal = {Annales de l'institut Fourier},
keywords = {normal forms; elementary divisors; Malgrange preparation theorem; matrix valued functions},
language = {eng},
number = {3},
pages = {865-892},
publisher = {Association des Annales de l'Institut Fourier},
title = {Preparation theorems for matrix valued functions},
url = {http://eudml.org/doc/75023},
volume = {43},
year = {1993},
}

TY - JOUR
AU - Dencker, Nils
TI - Preparation theorems for matrix valued functions
JO - Annales de l'institut Fourier
PY - 1993
PB - Association des Annales de l'Institut Fourier
VL - 43
IS - 3
SP - 865
EP - 892
AB - We generalize the Malgrange preparation theorem to matrix valued functions $F(t,x)\in C^\infty ({\bf R}\times {\bf R}^n)$ satisfying the condition that $t\mapsto \, {\rm det}\, F(t,0)$ vanishes to finite order at $t=0$. Then we can factor $F(t,x) = C(t,x)P(t,x)$ near (0,0), where $C(t,x)\in C^\infty $ is inversible and $P(t,x)$ is polynomial function of $t$ depending $C^\infty $ on $x$. The preparation is (essentially) unique, up to functions vanishing to infinite order at $x=0$, if we impose some additional conditions on $P(t,x)$. We also have a generalization of the division theorem, and analytic versions generalizing the Weierstrass preparation and division theorems.
LA - eng
KW - normal forms; elementary divisors; Malgrange preparation theorem; matrix valued functions
UR - http://eudml.org/doc/75023
ER -