On extension theory in \(L^ 2\)-spaces
In the context of singular perturbations of selfadjoint operators in \(L^2\)-spaces, some results have been obtained based on nonstandard analysis. In this paper, the author, using only standard analysis, develops an extension theory in \(L^2\)-spaces in a locally compact separable metric space to obtain the set of all selfadjoint extensions of some operators \(H\) (an example is the Laplacian in \(\mathbb{R}^n\)) restricted to the complement of a compact set \(N\) (which in the classical potential theory can be a closed set of capacity \(\geq 0\)).
singular perturbations of selfadjoint operators
scientific article; zbMATH DE number 763782