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.

引用

页数：8

共 50 条

[11] Linear operators in the theory of partial differential equations
Bergman, Stefan
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1943, 53 (1-3) : 130 - 155
[12] LINEAR PARTIAL DIFFERENTIAL OPERATORS AND GENERALIZED DISTRIBUTIONS
BJORCK, G
ARKIV FOR MATEMATIK, 1966, 6 (4-5): : 351 - &
[13] ON COMMUTING LINEAR PARTIAL-DIFFERENTIAL OPERATORS
HAINZL, J
ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1981, 38 (1-4): : 1 - 8
[14] Ideals of differential operators and transformations of linear partial differential equations
Kaptsov, O. V.
PROGRAMMING AND COMPUTER SOFTWARE, 2010, 36 (02) : 97 - 102
[15] Ideals of differential operators and transformations of linear partial differential equations
O. V. Kaptsov
Programming and Computer Software, 2010, 36 : 97 - 102
[16] NORMAL SOLVABILITY IN LINEAR PARTIAL-DIFFERENTIAL OPERATORS IN LOCAL WEIGHTED SOBOLEV SPACES
SAGRALOFF, B
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1979, 310 : 131 - 150
[17] Some estimates in Rn for linear partial differential operators
Tyurin, VM
DIFFERENTIAL EQUATIONS, 2000, 36 (08) : 1259 - 1261
[18] Some estimates in Rn for linear partial differential Φ+-operators
V. M. Tyurin
Differential Equations, 2000, 36 : 477 - 479
[19] ON THEORY OF LINEAR PARTIAL DIFFERENTIAL OPERATORS WITH ANALYTIC COEFFICIENTS
TREVES, F
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 137 (MAR) : 1 - &
[20] Some estimates inRn for linear partial differential operators
V. M. Tyurin
Differential Equations, 2000, 36 : 1259 - 1261

← 1 2 3 4 5 →