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

Carlos A. Berenstein; Qin Li Bao

Publicacions Matemàtiques (1994)

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

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topBerenstein, 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 > 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 > 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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