Vol. 61, No. 1, 1975

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Locality of the number of particles operator

M. Ann Piech

Vol. 61 (1975), No. 1, 259–262

We view the number of particles operator N as the infinitesimal generator of the Ornstein-Uhlenbeck semigroup in an abstract Wiener setting. It is shown that if two functions f, g in the domain of N agree a.e. on an open set 𝒪, then Nf = Ng on 𝒪. The restriction of N to a large core acts as an infinite dimensional partial differential operator L, and it is shown that L may be defined locally in an Lloc2 setting.

Mathematical Subject Classification
Primary: 81.47, 81.47
Received: 11 July 1975
Published: 1 November 1975
M. Ann Piech