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Zeitschrift für Analysis und ihre Anwendungen

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Volume 17, Issue 2, 1998, pp. 329–338
DOI: 10.4171/ZAA/825

Published online: 1998-06-30

On Persson’s Theorem in Local Dirichiet Spaces

Gabriele Grillo[1]

(1) Politecnica di Milano, Italy

Given a strongly local, regular and irreducible Dirichlet form $\mathcal E$, we prove a version of Persson’s theorem concerning the variational characterization of the bottom of the essential spectrum of the generator $H$ of $\mathcal E$. Such a result is then used to prove $L^p$-exponential decay of the "small eigenfunctions" of $H$.

Keywords: Local Dirichlet spaces, Persson’s theorem, small eigenfunctions

Grillo Gabriele: On Persson’s Theorem in Local Dirichiet Spaces. Z. Anal. Anwend. 17 (1998), 329-338. doi: 10.4171/ZAA/825