Diffusion semigroups on abstract Wiener space
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- by M. Ann Piech PDF
- Trans. Amer. Math. Soc. 166 (1972), 411-430 Request permission
Abstract:
The existence of a semigroup of solution operators associated with a second order infinite dimensional parabolic equation of the form $\partial u/\partial t = {L_x}u$ was previously established by the author. The present paper investigates the relationship between ${L_x}$ and the infinitesimal generator $\mathcal {U}$ of the semigroup. In particular, it is shown that $\mathcal {U}$ is the closure of ${L_x}$ in a natural sense. This in turn implies certain uniqueness results for both the semigroup and for solutions of the parabolic equation.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 166 (1972), 411-430
- MSC: Primary 47D05; Secondary 28A40
- DOI: https://doi.org/10.1090/S0002-9947-1972-0295141-3
- MathSciNet review: 0295141