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A Moment Characterization of B–Valued Generalized Functionals of White Noise

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Abstract

Kernel theorems are established for Banach space–valued multilinear mappings. A moment characterization theorem for Banach space–valued generalized functionals of white noise is proved by using the above kernel theorems. A necessary and sufficient condition in terms of moments is given for sequences of Banach space–valued generalized functionals of white noise to converge strongly. The integration is also discussed of functions valued in the space of Banach space–valued generalized functionals.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, P. R. China

    Cai Shi Wang

  2. Department of Mathematics, Huazhong University of Science and Technology, Wuhan 430074, P. R. China

    Zhi Yuan Huang

Authors
  1. Cai Shi Wang
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  2. Zhi Yuan Huang
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Correspondence to Cai Shi Wang.

Additional information

Supported by NSFC (10171035), NSF of Gansu Province (ZS021-A25-004-Z), and NWNU–KJCXGC-212, China

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Wang, C.S., Huang, Z.Y. A Moment Characterization of B–Valued Generalized Functionals of White Noise. Acta Math Sinica 22, 157–168 (2006). https://doi.org/10.1007/s10114-004-0523-z

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  • DOI: https://doi.org/10.1007/s10114-004-0523-z

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