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Factorization property of convolutions of white noise operators

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Abstract

We first study a general type of convolutions, parameterized by operators, on white noise functionals and study a relation between the convolution and the generalized Fourier-Mehler transform. Secondly, we extend the convolution of generalized white noise functionals to a convolution of white noise operators. Then, as factorization properties of the convolutions, we study a relation between the convolution and quantum generalized Fourier-Mehler transform.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Research Institute of Mathematical Finance, Chungbuk National University, Cheongju, 361-763, Korea

    Un Cig Ji

  2. Research Institute for Natural Science, Hanyang University, Seoul, 133-791, Korea

    Young Yi Kim

  3. Department of Mathematics, Chungbuk National University, Cheongju, 361-763, Korea

    Yoon Jung Park

Authors
  1. Un Cig Ji
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  2. Young Yi Kim
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  3. Yoon Jung Park
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Corresponding author

Correspondence to Un Cig Ji.

Additional information

Dedicated to Professor Kalyan B. Sinha on the occasion of his 70th birthday.

This work was supported by Basic Science Research Program through the NRF funded by the MEST (NRF-2013R1A1A2013712).

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Ji, U.C., Kim, Y.Y. & Park, Y.J. Factorization property of convolutions of white noise operators. Indian J Pure Appl Math 46, 463–476 (2015). https://doi.org/10.1007/s13226-015-0146-3

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  • DOI: https://doi.org/10.1007/s13226-015-0146-3

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