Abstract
We introduce a new Hilbert space HL, called Levy{Hilbert space, arising from the LLaplacian. This Hilbert space is used to construct a new Gel'fand triple called Levy{Gel'fand triple, which exhibits the essentially inflnite dimensional character of the Levy Laplacian. By using the fact that the usual trace and the Ltrace (being associated with an appropriate orthonormal system) coincide on the Lert space, we prove a theorem asserting that the Levy Laplacian and the Gross Laplacian coincide on the space of Ltest functions as continuous linear operators.
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