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Smooth perturbations of regular Dirichlet forms. (English) Zbl 0768.31009

Let \(\mu\) be a measure that does not charge sets of capacity zero. It is proved here that \(\mu\) is a smooth measure if and only if for a regular Dirichlet form \(h\), the domain of \(h+\mu\) is dense (with respect to the norm determined by \(h\)) in the domain of \(h\), or equivalently \(h+a\mu\) tends to \(h\) in the strong resolvent sense when \(a\) decreases to zero.
Reviewer: V.Anandam (Riyadh)

MSC:

31C25 Dirichlet forms
35J10 Schrödinger operator, Schrödinger equation
60J60 Diffusion processes
60J65 Brownian motion

Keywords:

smooth measure
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References:

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