Two classes of extensions for generalized Schrödinger operators are considered. One is the Markovian self-adjoint extensions and the other is the extensions in Silverstein's sense. We prove that these classes of extensions are identical. As its application, some properties of drift transformations of Brownian motion are derived.
- Dirichlet forms
- Drift transformations of Brownian motion
- Extensions in Silverstein's sense
- Generalized Schrödinger operators
- Markovian self-adjoint extensions
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