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Hermite expansions of some tempered distributions

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Abstract

We compute Hermite expansions of some tempered distributions by using the Bargmann transform. In other words, we calculate the Taylor expansions of the corresponding entire functions. Our method of computations seems to be superior to the direct computations in the shifts of singularities and the higher dimensional cases.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Education, University of the Ryukyus, Nishihara, Okinawa, 903-0213, Japan

    Hiroyuki Chihara

  2. Graduate School of Mathematics, Nagoya University, Nagoya, Aichi, 464-8602, Japan

    Takashi Furuya

  3. Department of Science, Graduate School of Science and Technology for Innovation, Yamaguchi University, Yamaguchi, Yamaguchi, 753-8512, Japan

    Takumi Koshikawa

Authors
  1. Hiroyuki Chihara
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  2. Takashi Furuya
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  3. Takumi Koshikawa
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Corresponding author

Correspondence to Hiroyuki Chihara.

Additional information

Hiroyuki Chihara is supported by the JSPS Grant-in-Aid for Scientific Research #16K05221.

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Chihara, H., Furuya, T. & Koshikawa, T. Hermite expansions of some tempered distributions. J. Pseudo-Differ. Oper. Appl. 9, 105–124 (2018). https://doi.org/10.1007/s11868-017-0211-2

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  • DOI: https://doi.org/10.1007/s11868-017-0211-2

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