Interpolating varieties for weighted spaces of entire functions in Cn.

Berenstein, Carlos A., and Bao, Qin Li. "Interpolating varieties for weighted spaces of entire functions in Cn.." Publicacions Matemàtiques 38.1 (1994): 157-173. <http://eudml.org/doc/41200>.

@article{Berenstein1994,
abstract = {We prove in this paper that a given discrete variety V in Cn is an interpolating variety for a weight p if and only if V is a subset of the variety \{ξ ∈ Cn: f1(ξ) = f2(ξ) = ... = fn(ξ) = 0\} of m functions f1, ..., fm in the weighted space the sum of whose directional derivatives in absolute value is not less than ε exp(-Cp(ζ)), ζ ∈ V for some constants ε, C &gt; 0. The necessary and sufficient conditions will be also given in terms of the Jacobian matrix of f1, ..., fm. As a corollary, we solve an open problem posed by Berenstein and Taylor about interpolation for discrete varieties.},
author = {Berenstein, Carlos A., Bao, Qin Li},
journal = {Publicacions Matemàtiques},
keywords = {Función entera; Variable compleja; Conjuntos de interpolación; Funciones de peso; entire function; interpolating variety},
language = {eng},
number = {1},
pages = {157-173},
title = {Interpolating varieties for weighted spaces of entire functions in Cn.},
url = {http://eudml.org/doc/41200},
volume = {38},
year = {1994},
}

TY - JOUR
AU - Berenstein, Carlos A.
AU - Bao, Qin Li
TI - Interpolating varieties for weighted spaces of entire functions in Cn.
JO - Publicacions Matemàtiques
PY - 1994
VL - 38
IS - 1
SP - 157
EP - 173
AB - We prove in this paper that a given discrete variety V in Cn is an interpolating variety for a weight p if and only if V is a subset of the variety {ξ ∈ Cn: f1(ξ) = f2(ξ) = ... = fn(ξ) = 0} of m functions f1, ..., fm in the weighted space the sum of whose directional derivatives in absolute value is not less than ε exp(-Cp(ζ)), ζ ∈ V for some constants ε, C &gt; 0. The necessary and sufficient conditions will be also given in terms of the Jacobian matrix of f1, ..., fm. As a corollary, we solve an open problem posed by Berenstein and Taylor about interpolation for discrete varieties.
LA - eng
KW - Función entera; Variable compleja; Conjuntos de interpolación; Funciones de peso; entire function; interpolating variety
UR - http://eudml.org/doc/41200
ER -