Potentials of zero radius and Carleman operators
type: Item
instance of: scholarly article
title: Potentials of zero radius and Carleman operators
zbMATH Open document ID: 0899.47021
DOI: 10.1007/BF02107328
author: V. A. Margulis
author: I. I. Chuchaev
author: V. A. Geiler
published in: Siberian Mathematical Journal
publication date: 1998-11-02T00:00:00Z
review text: Let \(\Omega\) be an open subset of \(\mathbb{R}^\nu\); \(H_0\) is a selfadjoint operator in \(L^2(\Omega)\), and \(A\) is a subset of \(\Omega\) satisfying the uniform discreteness condition \[ d(A)\equiv \inf\{| \alpha-\beta|: \alpha,\beta\in A,\;\alpha\neq\beta\}> 0. \] Let \(D(H_0)\) be the domain of \(H_0\), \[ D_A= \{\varphi\in D(H_0): \varphi(\alpha)=0\;\forall\alpha\in A\}. \] An unconditional basis in the defect subspace of the operator \(H_0| D_A\) and the Green function for the selfadjoint extension of its closure are constructed.
reviewed by: Boris Rubin
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 47A20
zbMATH DE Number: 923539
zbMATH Keywords: Carleman operators
zbMATH Keywords: selfadjoint operator
zbMATH Keywords: uniform discreteness condition
zbMATH Keywords: unconditional basis
zbMATH Keywords: defect subspace
zbMATH Keywords: Green function
zbMATH Keywords: selfadjoint extension
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02107328
OpenAlex ID: W2024867658
description: scientific article; zbMATH DE number 923539