Parametrization of supersingular perturbations in the method of rigged Hilbert spaces

A classification of bounded below supersingular perturbations à of a self-adjoint operator A ⩾ 1 is suggested. In the A-scale of Hilbert spaces \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{H}_{ - k} \sqsupset \mathcal{H} \sqsupset \mathcal{H}_k $$ \end{document} = Dom Ak/2, k > 0, a parametrization of operators à in terms of bounded mappings S: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{H}_k \to \mathcal{H}_{ - k} $$ \end{document} such that ker S is dense in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathcal{H}_{k/2} $$ \end{document} is obtained.