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- Publisher
- Springer Journals
- Copyright
- Copyright © 2005 by Springer Science+Business Media, Inc.
- Subject
- Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/s10440-005-9000-7
- Publisher site
- See Article on Publisher Site
Abstract
Consider the Lévy white noise space $${\left( {{\user1{\mathcal{S}}}*,\mu } \right)}$$ where $${\user1{\mathcal{S}}}*$$ is the space of Schwartz tempered distributions over $$\mathbb{R}^{d} $$ and μ is a Lévy white noise measure lifted from a one-dimensional infinitely divisible distribution with finite moments. The classical polynomials of Meixner's type are distinguished through a special form of their generating functions. By lifting the generating function of Meixner orthogonal polynomials, we construct the renormalization kernels explicitly in a unified way. Moreover, we define inner products in n-particle spaces in terms of traces on the ‘diagonals’ and obtain a unified explicit chaotic representation of Lévy–Meixner white noise functionals in terms of interacting Fock spaces. The interacting feature is completely determined by a function g which is referred to as ‘interaction exponent’. This method enables us to easily recapture the general form of Lévy–Meixner field operators.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Oct 11, 2005