English

Quantum Gross Laplacian and Applications

Probability 2008-04-25 v1 Functional Analysis

Abstract

In this paper, we introduce and study a noncommutative extension of the Gross Laplacian, called quantum Gross Laplacian. Then, applying the quantum Gross Laplacian to the particular case where the operator is the multiplication operator, we find a relation between classical and quantum Gross Laplacian. As application, we give explicit solution of linear quantum white noise differential equation. In particular, we give a explicit solution of the quantum Gross heat equation.

Cite

@article{arxiv.0804.3938,
  title  = {Quantum Gross Laplacian and Applications},
  author = {Habib Ouerdiane and Samah Horrigue},
  journal= {arXiv preprint arXiv:0804.3938},
  year   = {2008}
}
R2 v1 2026-06-21T10:34:18.883Z