Title

On Fourier transform of generalized Brownian functionals

Document Type

Article

Publication Date

1-1-1982

Abstract

Let (L2) B ̇- and (L2) b ̇- be the spaces of generalized Brownian functionals of the white noises Ḃ and ḃ, respectively. A Fourier transform from (L2) B ̇- into (L2) b ̇- is defined by φ{symbol}̂(ḃ) = ∫S*: exp[-i ∫Rḃ(t) Ḃ(t) dt]: b ̇φ{symbol}( B ̇) dμ( B ̇), where : : b ̇ denotes the renormalization with respect to ḃ and μ is the standard Gaussian measure on the space S* of tempered distributions. It is proved that the Fourier transform carries Ḃ(t)-differentiation into multiplication by iḃ(t). The integral representation and the action ofφ{symbol}̂ as a generalized Brownian functional are obtained. Some examples of Fourier transform are given. © 1982.

Publication Source (Journal or Book title)

Journal of Multivariate Analysis

First Page

415

Last Page

431

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