The Domain of a Generator and the Intertwining Property
The generator of a semigroup is fundamental but it is rather difficult to give a precise characterization to its domain. Some generators are well studied, and we can give them precise domains. For example, the Laplacian on ℝd and the Ornstein-Uhlenbeck operator on the Wiener space inL 2 setting are well known. In fact, the domain of the Laplacian on W’ is the Sobolev space H2(ts domain. Some generators are well studied, and we can give them precise domains. For example, the Laplacian on ℝd). A similar result holds for the Ornstein-Uhlenbeck operator.
KeywordsSobolev Inequality Generator Domain Dirichlet Form Precise Characterization Logarithmic Sobolev Inequal
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