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Polynomial interpolation and residue currents
Complex Variables and Elliptic Equations ( IF 0.6 ) Pub Date : 2021-03-15 , DOI: 10.1080/17476933.2021.1897796
Jimmy Johansson 1
Affiliation  

We show that a global holomorphic section of O(d) restricted to a closed complex subspace XPn has an interpolant if and only if it satisfies a set of moment conditions that involves a residue current associated with a locally free resolution of OX. When X is a finite set of points in CnPn this can be interpreted as a set of linear conditions that a function on X has to satisfy in order to have a polynomial interpolant of degree at most d.



中文翻译:

多项式插值和剩余电流

我们证明了一个全局全纯截面(d)受限于一个封闭的复子空间Xn有一个插值当且仅当它满足一组矩条件,这些条件涉及与局部自由分辨率相关的残余电流X. 当XCnn这可以解释为X上的函数必须满足的一组线性条件,以便具有最多d次的多项式插值。

更新日期:2021-03-15
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