Quantum Lévy Laplacian and associated heat equation

Un Cig Ji, Nobuaki Obata, Habib Ouerdiane

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


As a non-commutative extension of the Lévy Laplacian for entire functions on a nuclear space, we define the quantum Lévy Laplacian acting on white noise operators. We solve a heat type equation associated with the quantum Lévy Laplacian and study its relation to the classical Lévy heat equation. The solution to the quantum Lévy heat equation is obtained also from a normal-ordered white noise differential equation involving the quadratic quantum white noise.

Original languageEnglish
Pages (from-to)31-54
Number of pages24
JournalJournal of Functional Analysis
Issue number1
Publication statusPublished - 2007 Aug 1


  • Heat equation
  • Quantum Lévy Laplacian
  • Quantum white noise
  • White noise operator
  • Wick symbol


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