Title

Diagonalization of the Lévy Laplacian and related stable processes

Document Type

Article

Publication Date

9-1-2002

Abstract

Eigenfunctions of the Lévy Laplacian with an arbitrary real number as an eigenvalue are constructed by means of a coordinate change of white noise distributions. The Lévy Laplacian is diagonalized on the direct integral Hilbert space of such eigenfunctions and the corresponding equi-continuous semigroup is obtained. Moreover, an infinite dimensional stochastic process related to the Lévy Laplacian is constructed from a one-dimensional stable process.

Publication Source (Journal or Book title)

Infinite Dimensional Analysis, Quantum Probability and Related Topics

First Page

317

Last Page

331

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