Local Linear Dependence of Linear Partial Differential Operators

被引：0

作者：

J. Cimprič

机构：

[1] University of Ljubljana,Department of Mathematics Faculty of Mathematics and Physics

来源：

Integral Equations and Operator Theory | 2018年 / 90卷

关键词：

Operator theory (linear partial differential operators, local linear dependence); Numerical mathematics (multivariate Hermite interpolation); Algebraic geometry (nullstellensatz, noncommutative generalizations);

D O I：

暂无

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学科分类号：

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.

引用

共 17 条

[1]

Ambrozie C(2010)An upper bound on the dimension of the reflexivity closure Proc. Am. Math. Soc. 138 1721-1731

[2]

Kuzma B(2013)A local-global principle for linear dependence of noncommutative polynomials Isr. J. Math. 193 71-82

[3]

Müller V(1999)On locally linearly dependent operators and derivations Trans. Am. Math. Soc. 351 1257-1275

[4]

Brešar M(2003)Matrix inequalities: a symbolic procedure to determine convexity automatically Integral Equ. Oper. Theory 46 399-454

[5]

Klep I(2013)A noncommutative real nullstellensatz corresponds to a noncommutative real ideal: algorithms Proc. Lond. Math. Soc. (3) 106 1060-1086

[6]

Brešar M(2013)A real nullstellensatz for free modules J. Algebra 396 143-150

[7]

Šemrl P(2000)Multivariate Hermite interpolation by algebraic polynomials: a survey J. Comput. Appl. Math. 122 167-201

[8]

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