Point interactions in \(L^ p\)
Let \(N\in \{1,2,3\}\), and \(1<p<\infty\) (\(3/2<p<3\) if \(N=3\)). The authors consider the operator \(-\Delta\) defined on \(\{u\in C_ 0^ \infty (\mathbb{R}^ N)\): \(u(0)=0\}\). A certain selfadjoint extension of \(-\Delta\) on \(L^ 2(\mathbb{R}^ N)\), called a point interaction, was studied by \textit{S. Albeverio}, \textit{F. Gesztesy}, \textit{R. Høegh-Krohn} and \textit{H. Holden} [Solvable models in quantum mechanics (1988; Zbl 0679.46057)]. The authors study analogous closed extensions on \(L^ p(\mathbb{R}^ N)\) which they view as analogues of the point interactions. Their study is based on a more general method for the perturbation of infinitesimal generators of uniformly continuous semigroups.
perturbation of infinitesimal generators of uniformly continuous semigroups
scientific article; zbMATH DE number 167679
scientific article