论文标题
用于增生和（广义的）单调设置值运算符的逻辑METATHEOREMS
Logical metatheorems for accretive and (generalized) monotone set-valued operators
论文作者
论文摘要
增生性和单调操作员理论是非线性功能分析的中心分支，构成了功能空间之间集合值映射的抽象研究。本文介绍了某些大型运算符的计算属性，即增强和（广义）单调设置值。特别是，我们为该领域开发（并扩展）证明挖掘的理论框架，这是一种数学逻辑中的计划，旨在从主流文献中从表面上提取计算信息。为此，我们建立了逻辑元素，以保证和量化与积聚和（广义的）单调设置值算子有关的定理的计算内容。一方面，我们的结果统一了许多近期案例研究，而它们还以证明理论的概念在另一个案例中提供了中心分析概念的特征，这在证明理论方面提供了至关重要的观点，即对证明挖掘在这些分支机构的未来应用中所需的定量假设提供了关键的观点。
Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of set-valued mappings between function spaces. This paper deals with the computational properties of certain large classes of operators, namely accretive and (generalized) monotone set-valued ones. In particular, we develop (and extend) for this field the theoretical framework of proof mining, a program in mathematical logic that seeks to extract computational information from prima facie `non-computational' proofs from the mainstream literature. To this end, we establish logical metatheorems that guarantee and quantify the computational content of theorems pertaining to accretive and (generalized) monotone set-valued operators. On one hand, our results unify a number of recent case studies, while they also provide characterizations of central analytical notions in terms of proof theoretic ones on the other, which provides a crucial perspective on needed quantitative assumptions in future applications of proof mining to these branches.
