Harmonic analysis in infinite dimension |
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Authors: | Denis Feyel Arnaud de la Paradelle |
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Institution: | (1) Université Paris VI, Tour U6-0, 4ème étage, 4 Place Jussieu BP 186, F-75252 Paris Cedex 05, France |
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Abstract: | We study the Hermite transform onL
2() where is a Gaussian measure on a Lusin locally convex spaceE. We are then lead to a Hilbert space () 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 . 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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Keywords: | 28C20 13C15 44A10 43A99 46A12 46F05 46F25 46E25 |
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