The spectrum of the Hilbert space valued second derivative with general self-adjoint boundary conditions
type: Item
instance of: scholarly article
title: The spectrum of the Hilbert space valued second derivative with general self-adjoint boundary conditions
zbMATH Open document ID: 1322.34048
author: Joachim von Below
author: Delio Mugnolo
published in: Linear Algebra and its Applications
publication date: 2014-02-19T00:00:00Z
full work available at URL: https://arxiv.org/abs/1209.0932
review text: This work is concerned with the spectral structure of the potential-less Laplace operator acting on a compact graph with either Kirchhoff and continuity conditions at interior vertices, or so called anti-Kirchhoff conditions, and suitable boundary conditions at terminal vertices. The authors show that the spectrum (eigenvalues along with their multiplicities) determine uniquely: the number of vertices of the graph; the number of components of the graph; the number of edges of the graph and numbers of bipartite and non-bipartite components.
Mathematics Subject Classification ID: 34B45
Mathematics Subject Classification ID: 34A55
zbMATH DE Number: 6259651
zbMATH Keywords: quantum graphs
zbMATH Keywords: differential operators on graphs
zbMATH Keywords: inverse problems
reviewed by: Bruce A. Watson
MaRDI profile type: Publication
OpenAlex ID: W1965435251
arXiv ID: 1209.0932
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DOI: 10.1016/J.LAA.2013.05.011
description: scientific article