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Motivated by the concept of “generating operators” for a countable family of operators introduced in the recent paper (arXiv:2306.16800), we find a method to reconstruct the Rankin–Cohen brackets from a very simple multivariable contour integral, and obtain a new proof of their covariance. We also establish a closed formula of the “generating operator” for the Rankin–Cohen brackets in full generality.

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A Short Proof for Rankin–Cohen Brackets and Generating Operators

  • 会议论文

  • 发表日期：

    2025年

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  • Toshiyuki Kobayashi,
  • Michael Pevzner

摘要

Motivated by the concept of “generating operators” for a countable family of operators introduced in the recent paper (arXiv:2306.16800), we find a method to reconstruct the Rankin–Cohen brackets from a very simple multivariable contour integral, and obtain a new proof of their covariance. We also establish a closed formula of the “generating operator” for the Rankin–Cohen brackets in full generality.