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Generalized Radon Transform and Lévy’s Brownian Motion, I*)

Published online by Cambridge University Press:  22 January 2016

Akio Noda
Akio Noda*
Affiliation:
Department of Mathematics Aichi University of Education, Kariya 448, Japan
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In connection with a Gaussian system X = {X(x); x ∈ M} called Lévy’s Brownian motion (Definition 1), we shall introduce two integral transformations of special type—one is a generalized Radon transform R on a measure space (M, m), and the other is a dual Radon transform R* on another measure space (H, v) such that H ⊂ 2M, the set of all subsets of M (Definition 2). To each Lévy’s Brownian motion X, there is attached a distance d(x, y):= E[(X(x) — X(y)2] on M having a notable property named L1-embeddability. The above measure v on H is then chosen to satisfy

where Δ stands for the symmetric difference.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 105 , March 1987 , pp. 71 - 87
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1987

Footnotes

*)

Contribution to the research project Reconstruction, Ko 506/8-1, of the German Research Council (DFG), directed by Professor D. Kölzow, Erlangen.

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