On partition of energy for uniformly propagative systems |
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Authors: | David Goldstein Costa |
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Affiliation: | Departamento de Matemàtica, Universidade de Brasilia, Brasilia, Brasil |
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Abstract: | This paper discusses the smoothness properties of partitions of unity which are available for any real separable Banach space B which is the support space for a mean zero Gaussian measure μ. Elements of the partition of unity are infinitely differentiable in the directions in which μ translates to an equivalent measure. The set of such directions forms a Hilbert subspace H of B, and the derivatives of the partition functions are shown to take values in the n-fold symmetric tensor product of H. |
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