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We present a decomposition principle for general regular Dirichlet forms satisfying a spatial local compactness condition. We use the decomposition principle to derive a Persson type theorem for the corresponding Dirichlet forms. In particular our setting covers Laplace–Beltrami operators on Riemannian manifolds, and Dirichlet forms associated to -stable processes in Euclidean space.
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H. Daniel Lenz, Peter Stollmann, On the decomposition principle and a Persson type theorem for general regular Dirichlet forms. J. Spectr. Theory 9 (2019), no. 3, pp. 1089–1113