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Potential Analysis

, Volume 9, Issue 4, pp 351–382 | Cite as

Polynômes Harmoniques sur L'Espace du Bruit Blanc

  • Claude Martini
Article
  • 28 Downloads

Abstract

Let \(\mathcal{P}\) denote the space of harmonic polynomial of \(\mathbb{R}\)\(\mathbb{N}\). We study some properties of \(\mathcal{P}\) on the white noise space. We show that harmonic polynomials are characterized by an invariance property with respect to the S-transform, and that the closure\(\overline {\mathcal{P}}\) (S)harm of \(\mathcal{P}\)harm in Hida's test-functionnals topology is exactly the kernel of the Gross Laplacian ΔG. Lastly we show that Ker ΔG is strictly contained in the space of functionnals of (S) which remain fixed under S-transform.

White noise-harmonic polynomials-Cross 

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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Claude Martini
    • 1
  1. 1.Equipe D'Analyse et ProbabilitésUniversité d'Evry-Val-d'EssonneEVERY CedexFrance;

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