AI 中文总结
研究线性关系的单参数半群理论，引入d.m.o.关系概念，建立其半群生成元刻画，推广Hille - Yosida和Lumer - Phillips定理，为线性关系单参数半群特性提供新视角。
AI 中文摘要
本文发展了线性关系的单参数半群理论，引入了定义域多值正交（d.m.o.）关系的概念。我们建立了一致连续和强连续半群生成元的完整刻画，分别表明它们是极大和稠d.m.o.关系。此外，Hille - Yosida和Lumer - Phillips定理被推广到这个一般情形，给出了生成收缩\(C_0\)半群（识别为极大反积累关系）和酉算子（反自伴关系）的充要条件。这个严格框架为线性关系的单参数半群的特性提供了新的视角。
英文摘要
This article develops a theory of one-parameter semigroups for linear relations, introducing the notion of domain-multivalued orthogonal (d.m.o.) relations. We establish complete characterizations for generators of uniformly and strongly continuous semigroups, showing them to be maximal and densely d.m.o. relations, respectively. Furthermore, the Hille-Yosida and Lumer-Phillips theorems are extended to this general setting, providing necessary and sufficient conditions for generating $C_0$-semigroups of contractions (identified as maximal anti-accumulative relations) and unitary operators (anti-selfadjoint relations). This rigorous framework sheds new light on the peculiarities of one-parameter semigroups for linear relations.
