Local Linear Dependence of Linear Partial Differential Operators

被引：1
|
作者：
Cimpric, J. [1 ]
机构：
[1] Univ Ljubljana, Fac Math & Phys, Dept Math, Jadranska 21, Ljubljana 1000, Slovenia
来源：
INTEGRAL EQUATIONS AND OPERATOR THEORY | 2018年 / 90卷 / 03期
关键词：
Operator theory (linear partial differential operators; local linear dependence); Numerical mathematics (multivariate Hermite interpolation); Algebraic geometry (nullstellensatz; noncommutative generalizations); REAL NULLSTELLENSATZ;
D O I：
10.1007/s00020-018-2466-2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that any finite set of linear partial differential operators with continuous coefficients is linearly dependent if and only if it is locally linearly dependent. It follows that the reflexive closure of any finite set of such operators is equal to its linear span. The last statement can be rephrased as a weak nullstellensatz for linear partial differential operators.
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页数：8
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