Title

Lévy Laplacian of generalized functions on a nuclear space

Document Type

Article

Publication Date

1-1-1990

Abstract

The Lévy Laplacian ΔF(ξ) = limN→∞N-1∑n = 1N 〈F″(ξ),en⊗ en〉 is shown to be equal to (i) ∝TF″s″(ξ;t)dt, where Fs″ is the singular part of F″, and (ii) 2limρ{variant}→0ρ{variant}-2(MF(ξ,ρ{variant})-F(ξ)), where MF is the spherical mean of F. It is proved that regular polynomials are Δ-harmonic and possess the mean value property. A relation between the Lévy Laplacian Δ and the Gross Laplacian ΔGF(ξ) = ∑n = 1∞=〈F″(ξ),en⊗ en〉 is obtained. An application to white noise calculus is discussed. © 1990.

Publication Source (Journal or Book title)

Journal of Functional Analysis

First Page

74

Last Page

92

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