A short proof for Rankin--Cohen brackets and generating operators
- Resource Type
- Working Paper
- Authors
- Kobayashi, Toshiyuki; Pevzner, Michael
- Source
- Subject
- Mathematics - Representation Theory
Mathematics - Classical Analysis and ODEs
Mathematics - Number Theory
47B38, Secondary 11F11, 22E45, 32A27, 30H10, 33C45, 43A85
- Language
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.