Abstract
We study the Hermite transform onL 2(μ) where μ is a Gaussian measure on a Lusin locally convex spaceE. We are then lead to a Hilbert space (ℋ) of analytic functions onE which is also a natural range for the Laplace transform. LetB be a convenient Hilbert-Schmidt operator on the Cameron-Martin spaceH of μ. There exists a natural sequence Cap n of capacities onE associated toB. This implies the Kondratev-Yokoi theorem about positive linear forms on the Hida test-functions space.
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Feyel, D., de la Paradelle, A. Harmonic analysis in infinite dimension. Potential Anal 2, 23–36 (1993). https://doi.org/10.1007/BF01047671
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DOI: https://doi.org/10.1007/BF01047671