A measure-theoretical approach to the nuclear and inductive spectral theorems (Q2572179)

In the present article, a revision of fundamental results concerning Gelfand-Kostyuchenko rigged Hilbert space is given. In particular, the authors give new versions of inductive and nuclear spectral theorems, which provide an explicit expression for generalized eigenvectors of normal operators in terms of certain Radon-Nikodym differentiation of a measure of the direct integral (which is the spectral representation of the Hilbert space on which a normal operator acts) by measures generated by an ordered set of cyclic vectors from the Hilbert space.