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

Rüdiger W. Braun; Reinhold Meise; B. Alan Taylor

RACSAM (2003)

- Volume: 97, Issue: 2, page 189-208
- ISSN: 1578-7303

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topBraun, 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 -

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