Functions of countable families of commuting selfadjoint operators. (English) Zbl 0940.47013
A function of a commuting family of selfadjoint operators is defined via a spectral integral. In its turn, the resulting operator has its own spectral measure. The author studies its structure and obtains an expansion with respect to its generalized eigenvectors. A possibility of the approximation by cylindrical functions is also established.
Reviewer: A.N.Kochubei (Kyïv)
MSC:
47A60 | Functional calculus for linear operators |
47A70 | (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces |