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The Domain of a Generator and the Intertwining Property

  • Ichiro Shigekawa
Chapter
Part of the Trends in Mathematics book series (TM)

Abstract

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.

Keywords

Sobolev Inequality Generator Domain Dirichlet Form Precise Characterization Logarithmic Sobolev Inequal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Ichiro Shigekawa
    • 1
  1. 1.Department of Mathematics Graduate School of SciencesKyoto UniversityKyotoJapan

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