Rankin-Cohen brackets on pseudodifferential operators
SCIE
SCOPUS
- Title
- Rankin-Cohen brackets on pseudodifferential operators
- Authors
- Choie, Y; Lee, MH
- Date Issued
- 2007-02-15
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Abstract
- Pseudodifferential operators that are invariant under the action of a discrete subgroup Gamma of SL(2, R) correspond to certain sequences of modular forms for Gamma. 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. (c) 2006 Elsevier Inc. All rights reserved.
- Keywords
- modular forms; pseudodifferential operators; Jacobi-like forms; Rankin-Cohen brackets; Jacobi forms; MODULAR-FORMS; JACOBI
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/23666
- DOI
- 10.1016/j.jmaa.2006.03.048
- ISSN
- 0022-247X
- Article Type
- Article
- Citation
- JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol. 326, no. 2, page. 882 - 895, 2007-02-15
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