Point interactions in \(L^ p\)
type: Item
instance of: scholarly article
title: Point interactions in \(L^ p\)
zbMATH Open document ID: 0792.47033
DOI: 10.1007/BF02573568
author: Wim Caspers
author: Philippe Clément
published in: Semigroup Forum
publication date: 1993-05-16T00:00:00Z
full work available at URL: https://eudml.org/doc/135233
review text: 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.
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 47D06
Mathematics Subject Classification ID: 47N50
zbMATH DE Number: 167679
zbMATH Keywords: selfadjoint extension
zbMATH Keywords: perturbation of infinitesimal generators of uniformly continuous semigroups
reviewed by: H. Bercovici
MaRDI profile type: Publication
cites work: Q4073917
cites work: Q3994511
cites work: On abstract parabolic fundamental solutions
cites work: Scattering from generalized point interactions using self-adjoint extensions in Pontryagin spaces
cites work: Q3764747
cites work: Q3721264
cites work: Q3781625
cites work: Q4010839
cites work: Q5562752
OpenAlex ID: W1991873086
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description: scientific article; zbMATH DE number 167679