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http://hdl.handle.net/10773/38324
Title: | Global operator calculus on spin groups |
Author: | Cerejeiras, P. Ferreira, M. Kähler, U. Wirth, J. |
Keywords: | Spin group Spin representations Difference operators Pseudo-differential operators Fourier transform Microlocal analysis Elliptic operators Global hypoellipticity |
Issue Date: | 2023 |
Publisher: | Springer |
Abstract: | In this paper, we use the representation theory of the group Spin(m) to develop aspects of the global symbolic calculus of pseudo-differential operators on Spin(3) and Spin(4) in the sense of Ruzhansky–Turunen–Wirth. A detailed study of Spin(3) and Spin(4)-representations is made including recurrence relations and natural differential operators acting on matrix coefficients. We establish the calculus of left-invariant differential operators and of difference operators on the group Spin(4) and apply this to give criteria for the subellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of first and second order globally hypoelliptic differential operators are given, including some that are locally neither invertible nor hypoelliptic. The paper presents a particular case study for higher dimensional spin groups. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/38324 |
DOI: | 10.1007/s00041-023-10015-5 |
ISSN: | 1069-5869 |
Publisher Version: | https://link.springer.com/article/10.1007/s00041-023-10015-5 |
Appears in Collections: | CIDMA - Artigos CHAG - Artigos |
Files in This Item:
File | Description | Size | Format | |
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s00041-023-10015-5.pdf | 1.11 MB | Adobe PDF | View/Open |
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