Representations of hypercomplex systems with locally compact basis (Q1066067)

By following the general method developed by the first author, the results of Stone's and Sz. Nagy-Hille's type on the operator representations of commutative groups on Hilbert spaces are generalized by replacing the group by a more general structure called hypercomplex system. As particular cases are: compact groups, homogeneous spaces and the generalized translations defined by Sturm-Liouville equations on the half-axis. The main result is that any representation of a hypercomplex structure by (unbounded) normal operators on a Hilbert space may be written as an integral containing the characters of the structure.