An equivalent representation of the Jacobi field of a L\'evy process
Probability
2007-05-23 v1 Functional Analysis
Abstract
In [Yu.M. Berezansky, E. Lytvynov, D. A. Mierzejewski, Ukrainian Math. J. 55 (2003), 853--858 ], the Jacobi field of a L\'evy process was derived. This field consists of commuting self-adjoint operators acting in an extended (interacting) Fock space. However, these operators have a quite complicated structure. In this note, using ideas from [L. Accardi. U. Franz, M. Skeide, Comm. Math. Phys. 228 (2002), 123--150] and [E. Lytvynov, Infin. Dimen. Anal. Quant. Prob. Rel. Top. 7 (2004), 619--629], we obtain a unitary equivalent representation of the Jacobi field of a L\'evy process. In this representation, the operators act in a usual symmetric Fock space and have a much simpler structure.
Cite
@article{arxiv.math/0501450,
title = {An equivalent representation of the Jacobi field of a L\'evy process},
author = {Eugene Lytvynov},
journal= {arXiv preprint arXiv:math/0501450},
year = {2007}
}