# Interpolating varieties for weighted spaces of entire functions in Cn.

• Volume: 38, Issue: 1, page 157-173
• ISSN: 0214-1493

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## Abstract

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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.

## How to cite

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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 -

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