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
Recommended Citation
Kuo, H., Obata, N., & Saitô, K. (2002). Diagonalization of the Lévy Laplacian and related stable processes. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 5 (3), 317-331. https://doi.org/10.1142/S0219025702000882