Perturbation results for the local Phragmén-Lindelöf condition and stable homogeneous polynomials.

Braun, Rüdiger W., Meise, Reinhold, and Taylor, B. Alan. "Perturbation results for the local Phragmén-Lindelöf condition and stable homogeneous polynomials.." RACSAM 97.2 (2003): 189-208. <http://eudml.org/doc/40969>.

@article{Braun2003,
abstract = {The local Phragmén-Lindelöf condition for analytic varieties in complex n-space was introduced by Hörmander and plays an important role in various areas of analysis. Recently, new necessary geometric properties for a variety satisfying this condition were derived by the present authors. These results are now applied to investigate the homogeneous polynomials P with real coefficients that are stable in the following sense: Whenever f is a holomorphic function that is defined in some neighborhood of the origin, is real over real points, and has P as its localization at zero then the zero variety V(f) of f satisfies the local Phragmén-Lindelöf condition at the origin. It is shown that P can only be stable if V(P) satisfies the local Phragmén-Lindelöf condition at the origin and if, at each real point x in V(P) of modulus 1, the localization of P at x is either linear or an indefinite quadratic form. Further, for polynomials P in three variables it is shown that these necessary conditions are also sufficient for the stability of P and therefore characterize the table polynomials.},
author = {Braun, Rüdiger W., Meise, Reinhold, Taylor, B. Alan},
journal = {RACSAM},
keywords = {Funciones de varias variables complejas; Variedades analíticas; Funciones polinómicas; Funciones plurisubarmónicas},
language = {eng},
number = {2},
pages = {189-208},
title = {Perturbation results for the local Phragmén-Lindelöf condition and stable homogeneous polynomials.},
url = {http://eudml.org/doc/40969},
volume = {97},
year = {2003},
}

TY - JOUR
AU - Braun, Rüdiger W.
AU - Meise, Reinhold
AU - Taylor, B. Alan
TI - Perturbation results for the local Phragmén-Lindelöf condition and stable homogeneous polynomials.
JO - RACSAM
PY - 2003
VL - 97
IS - 2
SP - 189
EP - 208
AB - The local Phragmén-Lindelöf condition for analytic varieties in complex n-space was introduced by Hörmander and plays an important role in various areas of analysis. Recently, new necessary geometric properties for a variety satisfying this condition were derived by the present authors. These results are now applied to investigate the homogeneous polynomials P with real coefficients that are stable in the following sense: Whenever f is a holomorphic function that is defined in some neighborhood of the origin, is real over real points, and has P as its localization at zero then the zero variety V(f) of f satisfies the local Phragmén-Lindelöf condition at the origin. It is shown that P can only be stable if V(P) satisfies the local Phragmén-Lindelöf condition at the origin and if, at each real point x in V(P) of modulus 1, the localization of P at x is either linear or an indefinite quadratic form. Further, for polynomials P in three variables it is shown that these necessary conditions are also sufficient for the stability of P and therefore characterize the table polynomials.
LA - eng
KW - Funciones de varias variables complejas; Variedades analíticas; Funciones polinómicas; Funciones plurisubarmónicas
UR - http://eudml.org/doc/40969
ER -