The Lévy Laplacian as a self-adjoint operator (Q2735187)
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scientific article; zbMATH DE number 1640182
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Lévy Laplacian as a self-adjoint operator |
scientific article; zbMATH DE number 1640182 |
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25 March 2002
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Lévy Laplacian
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white noise functional
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infinite-dimensional Ornstein-Uhlenbeck process
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The Lévy Laplacian as a self-adjoint operator (English)
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The authors find a Hilbert space of generalized Gaussian white noise functionals, on which the Lévy Laplacian \(\Delta_L\) generates a self-adjoint operator. A key element is an explicit construction of eigenfunctions of \(\Delta_L\). A relation between the semigroup of operators generated by \(\Delta_L\) and the infinite-dimensional Ornstein-Uhlenbeck process is found.NEWLINENEWLINEFor the entire collection see [Zbl 0924.00055].
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