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Journal of Spectral Theory

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Volume 10, Issue 1, 2020, pp. 271–309
DOI: 10.4171/JST/292

Published online: 2019-10-18

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 10 (2020), 271-309. doi: 10.4171/JST/292