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On Closability of Directional Gradients

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Abstract

Let μ be a centred Gaussian measure on a separable real Banach space E, and let H be a Hilbert subspace of E. We provide necessary and sufficient conditions for closability in L p(E,μ) of the gradient D H in the direction of H. These conditions are further elaborated in case when the gradient D H corresponds to a bilinear form associated with a certain nonsymmetric Ornstein–Uhlenbeck operator. Some natural examples of closability and nonclosability are presented.

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Authors and Affiliations

  1. School of Mathematics, The University of New South Wales, Sydney, 2052, Australia

    B. Goldys

  2. Dipartimento di Matematica, Università di Pisa, Via F. Buonarroti n.2, 56127, Pisa, Italy

    F. Gozzi

  3. Department of Applied Mathematical Analysis, Technical University of Delft, P.O. Box 5031, 2600 GA, Delft, The Netherlands

    J.M.A.M. van Neerven

Authors
  1. B. Goldys
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  2. F. Gozzi
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  3. J.M.A.M. van Neerven
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Goldys, B., Gozzi, F. & van Neerven, J. On Closability of Directional Gradients. Potential Analysis 18, 289–310 (2003). https://doi.org/10.1023/A:1021832202659

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  • DOI: https://doi.org/10.1023/A:1021832202659

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