论文标题
Fredholm积分运营商的积极性和离散化
Positivity and discretization of Fredholm integral operators
论文作者
论文摘要
我们为矢量价值的弗雷德尔姆积分运算符及其常用的空间离散化提供了足够的条件，可以根据相应订单锥引起的顺序关系为正。事实证明，合理的Nyström方法可以保留阳性。在投影方法中，根据多项式，分段线性或特定的立方插值（搭配）以及在bubnov-galerkin方法中的分段常数基函数获得了最简单的方法。但是，对于使用二次样条或$ \ sinc $ collocation进行的饮食，我们证明了阳性是违反的。我们的结果是根据克雷因·罗特人运营商的特征款来说明的，并构成了非线性积分运营商相应研究的基础。
We provide sufficient conditions for vector-valued Fredholm integral operators and their commonly used spatial discretizations to be positive in terms of an order relation induced by a corresponding order cone. It turns out that reasonable Nyström methods preserve positivity. Among the projection methods, persistence is obtained for the simplest ones based on polynomial, piecewise linear or specific cubic interpolation (collocation), as well as for piecewise constant basis functions in a Bubnov-Galerkin approach. However, for semi-discretizations using quadratic splines or $\sinc$-collocation we demonstrate that positivity is violated. Our results are illustrated in terms of eigenpairs for Krein-Rutman operators and form the basis of corresponding investigations for nonlinear integral operators.
