L\'evy Laplacian for Square Roots of Measures
Abstract
L.Accardi shows that the Banach space of singed measures is homeomorphic to the Hilbert space formed by so-called root measures. In this paper, we redefine root measures in view of the theory of measures on infinite dimensional spaces, and introduce a notion of differentiation, Fourier transform, and convolution product for root measures, and examine those relations. We also study about L\'evy Laplacian on Wiener space as application. It is shown that the symbol of L\'evy Laplacian is equal to the quadratic variation of paths.
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