Subnormal operators whose adjoints have rich point spectrum

A generalized version of the Glauber–Klauder basic formula of quantum optics is shown to be valid for any cyclic subnormal operator S whose adjoint has a rich point spectrum σp(S∗) (in the sense that a semispectral measure of S vanishes on C∖σp∗(S∗)). It is exhibited that such operators always have analytic models. The point spectrum of the adjoint of a subnormal operator which satisfies a generalized version of the Glauber–Klauder formula is proved to be rich (in the above sense).