Commutative algebras of unbounded operators (original) (raw)

spectral representation for the operators N, and prove absolute continuity, and uniform multiplicity equal infinity. The exposition of the paper begins with the case d= 1. This is the unbounded version of the subnormal operators which have been studied extensively in the past in the case of bounded operators. We stress the differences between the theory for the bounded, and the unbounded case. Even in the case d= 1, the applications of the unbounded theory are surprising. (19X7 Academic Press. Inc C'onrents. I. Introduction. 2. Extending operators of semidetinite type. 3. Analytic vectors. 4. Algebras of operators. 5. Representations of the canonical commutation relations. 6. Bases in the Space 3. References.