Rankin-Cohen brackets on pseudodifferential operators
Jacobi forms, Jacobi-like forms, Modular forms, Pseudodifferential operators, Rankin-Cohen brackets
Journal of Mathematical Analysis and Applications
Pseudodifferential operators that are invariant under the action of a discrete subgroup Γ of SL (2, R) correspond to certain sequences of modular forms for Γ. Rankin-Cohen brackets are noncommutative products of modular forms expressed in terms of derivatives of modular forms. We introduce an analog of the heat operator on the space of pseudodifferential operators and use this to construct bilinear operators on that space which may be considered as Rankin-Cohen brackets. We also discuss generalized Rankin-Cohen brackets on modular forms and use these to construct certain types of modular forms. © 2006 Elsevier Inc. All rights reserved.
Original Publication Date
DOI of published version
Choie, Young Ju and Lee, Min Ho, "Rankin-Cohen brackets on pseudodifferential operators" (2007). Faculty Publications. 2649.