The Ornstein-Uhlenbeck semigroup in an infinite dimensional L2 setting

M. Ann Piech

doi:10.1016/0022-1236(75)90016-6

The Ornstein-Uhlenbeck semigroup in an infinite dimensional L² setting

M. Ann Piech

Mathematics

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

We study the number operator, N, of quantum field theory as a partial differential operator in infinitely many variables. Informally Nu(x) = -Δu(x) + x · grad u(x). A large core for N is constructed which is invariant under e^-tN and on which this informal expression may be given a precise and natural meaning.

Original language	English
Pages (from-to)	271-285
Number of pages	15
Journal	Journal of Functional Analysis
Volume	18
Issue number	3
DOIs	https://doi.org/10.1016/0022-1236(75)90016-6
State	Published - Mar 1975

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abstract = "We study the number operator, N, of quantum field theory as a partial differential operator in infinitely many variables. Informally Nu(x) = -Δu(x) + x · grad u(x). A large core for N is constructed which is invariant under e-tN and on which this informal expression may be given a precise and natural meaning.",

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AB - We study the number operator, N, of quantum field theory as a partial differential operator in infinitely many variables. Informally Nu(x) = -Δu(x) + x · grad u(x). A large core for N is constructed which is invariant under e-tN and on which this informal expression may be given a precise and natural meaning.

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The Ornstein-Uhlenbeck semigroup in an infinite dimensional L² setting

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