Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Smooth perturbations of regular Dirichlet forms

Author: Peter Stollmann
Journal: Proc. Amer. Math. Soc. 116 (1992), 747-752
MSC: Primary 31C25; Secondary 35J10
MathSciNet review: 1107277
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Abstract: Given a regular Dirichlet form $ \mathfrak{h}$, we prove that a measure $ \mu $ is smooth iff the domain of $ \mathfrak{h} + \mu $ is dense in the domain of $ \mathfrak{h}$ with respect to the form norm. The latter condition is in turn equivalent to the convergence of $ \mathfrak{h} + a\mu $ to $ \mathfrak{h}$.

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Keywords: Regular Dirichlet forms, smooth measures, Schrödinger operators
Article copyright: © Copyright 1992 American Mathematical Society