Magnetic interpretation of the nodal defect on graphs

Colin de Verdière, Yves

doi:10.2140/apde.2013.6.1235

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Magnetic interpretation of the nodal defect on graphs

Yves Colin de Verdière

Vol. 6 (2013), No. 5, 1235–1242

DOI: 10.2140/apde.2013.6.1235

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/

Vol. 6, No. 5, 2013