Regularized quasi-spectral distributions
The authors deal with a generalization of a spectral distribution, that they call a quasi-spectral distribution, that removes any density condition from the definition of a spectral distribution; in particular, the momentum needs not be densely defined, but a \(C^\infty({\mathbb{R}})\) functional calculus is constructed for it. Relations between regularized quasi-spectral distributions and \(C^\infty\) functional calculi as well as the relationship between the momentum of a certain class of \(C\)-regularized quasi-spectral distributions, and the generator of a generalization of strongly continuous groups, \(C\)-regularized groups and locally Lipschitz-continuous once-integrated \(C\)-regularized groups are considered. A generalization of Stone's theorem characterizes the momenta of certain (regularized) quasi-spectral distributions as generators of polynomially bounded once-integrated (regularized) groups.
Lipschitz-continuous once-integrated \(C\)-regularized groups
scientific article; zbMATH DE number 1226459