论文标题
urysohn和Hammerstein运营商H较旧的空间
Urysohn and Hammerstein operators on H"older spaces
论文作者
论文摘要
我们提出了一种面向申请的方法，用于urysohn和hammerstein积分运算符，该操作员作用于h“较旧的连续功能在紧凑的度量空间上的连续功能之间。这些非线性映射是通过涉及有限措施的抽象衡量标准的方法来提出的。这种柔性的设置是在同时使用的，这些柔性的设置与lebes e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e efers ass a persim a and e eik sely进行，同时是在lebes feel的范围内。使用稳定的正交/立方体规则（NYSTR“ OM方法）进行离散化。在合适的carath {é}内核函数上的气味条件下，建立了诸如定义良好的属性，界限，（完整的）连续性和连续性可不同。此外，Hammerstein操作员的特殊情况被理解为Fredholm和Nemytskii操作员的组成。尽管我们为Urysohn运营商的可不同性结果似乎是新的，但有关Nemytskii操作员的部分具有调查特征。最后，附录提供了一个相当全面的帐户，总结了在公制空间上定义的Hölder连续功能所需的预赛。
We present an application-oriented approach to Urysohn and Hammerstein integral operators acting between spaces of H"older continuous functions over compact metric spaces. These nonlinear mappings are formulated by means of an abstract measure theoretical integral involving a finite measure. This flexible setting creates a common framework to tackle both such operators based on the Lebesgue integral like frequently met in applications, as well as e.g.\ their spatial discretization using stable quadrature/cubature rules (Nystr"om methods). Under suitable Carath{é}odory conditions on the kernel functions, properties like well-definedness, boundedness, (complete) continuity and continuous differentiability are established. Furthermore, the special case of Hammerstein operators is understood as composition of Fredholm and Nemytskii operators. While our differentiability results for Urysohn operators appear to be new, the section on Nemytskii operators has a survey character. Finally, an appendix provides a rather comprehensive account summarizing the required preliminaries for Hölder continuous functions defined on metric spaces.
