Journal of Spectral Theory


List online-first JST articles | JST summary
Online access to the full text of Journal of Spectral Theory is restricted to the subscribers of the journal, who are encouraged to communicate their IP-address(es) to their agent or directly to the publisher at
subscriptions@ems-ph.org
Published online first: 2019-10-18
DOI: 10.4171/JST/292

Courant’s nodal domain theorem for positivity preserving forms

Matthias Keller[1] and Michael Schwarz[2]

(1) Universität Potsdam, Germany
(2) Universität Potsdam, Germany

We introduce a notion of nodal domains for positivity preserving forms. This notion generalizes the classical ones for Laplacians on domains and on graphs. We prove the Courant nodal domain theorem in this generalized setting using purely analytical methods.

Keywords: Nodal domain, eigenfunction, Dirichlet form, compact resolvent

Keller Matthias, Schwarz Michael: Courant’s nodal domain theorem for positivity preserving forms. J. Spectr. Theory Electronically published on October 18, 2019. doi: 10.4171/JST/292 (to appear in print)