2026/07/22 by Luis D. Regalado-Hernández, Josué I. Rios-Cangas
#math-ph #math.MP
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 C0-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.