Rankin-Cohen Brackets On Pseudodifferential Operators

Authors

Young Ju Choie, Pohang University of Science and TechnologyFollow
Min Ho Lee, University of Northern IowaFollow

Document Type

Article

Keywords

Jacobi forms, Jacobi-like forms, Modular forms, Pseudodifferential operators, Rankin-Cohen brackets

Journal/Book/Conference Title

Journal of Mathematical Analysis and Applications

Volume

326

Issue

2

First Page

882

Last Page

895

Abstract

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.

Department

Department of Mathematics

Original Publication Date

2-15-2007

DOI of published version

10.1016/j.jmaa.2006.03.048

Recommended Citation

Choie, Young Ju and Lee, Min Ho, "Rankin-Cohen Brackets On Pseudodifferential Operators" (2007). Faculty Publications. 2649.
https://scholarworks.uni.edu/facpub/2649