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.
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Matthias Keller, Michael Schwarz, Courant’s nodal domain theorem for positivity preserving forms. J. Spectr. Theory 10 (2020), no. 1, pp. 271–309DOI 10.4171/JST/292