A short proof for Rankin–Cohen brackets and generating operators

Kavli Affiliate: Toshiyuki Kobayashi

| First 5 Authors: Toshiyuki Kobayashi, Michael Pevzner, , ,

| Summary:

Motivated by the concept of lqlq{generating operators}rqrq 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 lqlq{generating
operator}rqrq for the Rankin–Cohen brackets in full generality.

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