Hermite expansions of some tempered distributions

  • Hiroyuki ChiharaEmail author
  • Takashi Furuya
  • Takumi Koshikawa


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.


Bargmann transform Tempered distribution Hermite expansion 

Mathematics Subject Classification

Primary 46F12 Secondary 33C45 47B32 


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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of EducationUniversity of the RyukyusNishiharaJapan
  2. 2.Graduate School of MathematicsNagoya UniversityNagoyaJapan
  3. 3.Department of Science, Graduate School of Science and Technology for InnovationYamaguchi UniversityYamaguchiJapan

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