Vol. 6, No. 5, 2013

Download this article
Download this article For screen
For printing
Recent Issues

Volume 13
Issue 6, 1605–1954
Issue 5, 1269–1603
Issue 4, 945–1268
Issue 3, 627–944
Issue 2, 317–625
Issue 1, 1–316

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
Magnetic interpretation of the nodal defect on graphs

Yves Colin de Verdière

Vol. 6 (2013), No. 5, 1235–1242
Abstract

We present a natural proof of a recent and surprising result of Gregory Berkolaiko interpreting the Courant nodal defect as a Morse index. This proof is inspired by a nice paper of Miroslav Fiedler published in 1975.

Keywords
operator on graphs, Schrödinger operators with magnetic fields, Morse index, Courant nodal theorem, Hill's operator
Mathematical Subject Classification 2010
Primary: 05C50, 35P05
Milestones
Received: 13 December 2012
Revised: 15 January 2013
Accepted: 14 February 2013
Published: 3 November 2013
Authors
Yves Colin de Verdière
Unité Mixte de Recherche CNRS-UJF 5582
Institut Fourier
BP 74
38402 Saint Martin d’Hères cedex
France
http://www-fourier.ujf-grenoble.fr/~ycolver/