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.
@article{urn:eudml:doc:41200,
title = {Interpolating varieties for weighted spaces of entire functions in Cn.},
journal = {Publicacions Matem\`atiques},
volume = {38},
year = {1994},
pages = {157-173},
mrnumber = {MR1291958},
zbl = {0820.32002},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41200}
}
Berenstein, Carlos A.; Bao, Qin Li. Interpolating varieties for weighted spaces of entire functions in Cn.. Publicacions Matemàtiques, Tome 38 (1994) pp. 157-173. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41200/