On the essential selfadjointness of Dirichlet operators on group-valued path space
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- by Ernesto Acosta PDF
- Proc. Amer. Math. Soc. 122 (1994), 581-590 Request permission
Abstract:
Let G be a compact Lie group with Lie algebra $\mathcal {G}$. Consider the Wiener measure P on the space \[ {W_G} = \{ g:[0,1] \to G,g {\text {continuous}},g(0) = e\} \] For each h in the Cameron-Martin space H over $\mathcal {G}$, let ${\partial _h}$ be the associated right invariant vector field over ${W_G}$ and let $\partial _h^ \ast$ be its adjoint with respect to P. We prove for a particular h that the space of functions on ${W_G}$ generated by ${C^\infty }$-cylindrical functions on ${W_G}$ together with one Gaussian random variable is a core for the Dirichlet operator $\partial _h^ \ast {\partial _h}$. This is the first step in proving the essential selfadjointness of the Number operator over group-valued path spaces in the natural presumed core.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 581-590
- MSC: Primary 58G32; Secondary 58D20, 60B15
- DOI: https://doi.org/10.1090/S0002-9939-1994-1195711-4
- MathSciNet review: 1195711