Theoretical and Natural Science
- The Open Access Proceedings Series for Conferences
Theoretical and Natural Science
Vol. 10, 17 November 2023
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Explicit form of Laplace-Beltrami operator on SO(3) in the view of Fourier analysis
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Abstract
Fourier analysis plays a central role in the modern physics, engineering, and mathematics itself. In the field of differential geometry, a Lie group G gives a symmetric structure, and one may apply the Fourier analysis by means of matrix-valued irreducible representations. Even though the entries of these irreducible representations are already shown to be the eigenfunctions of the Laplace-Beltrami operator, it is still desirable to consider a concrete example where both the operator and the irreducible representations can be computed explicitly. This study gives an explicit form of the Laplace-Beltrami operator on SO(3) using direct computations and show also that each entry of the irreducible representations o_n^ij is indeed an eigenfunction of this operator. Therefore, one can also find the application of the Fourier Analysis on differential equations, in this study Poisson’s equation as an example, using the Laplace-Beltrami operator as the corresponding differential operator. Overall, these results shed light on guiding further exploration of Fourier analysis.
Keywords
Fourier analysis on SO(3), Laplace-Beltrami operator on SO(3), poisson’s equation
References
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Data Availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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- Volume Title
- Proceedings of the 2023 International Conference on Mathematical Physics and Computational Simulation
- ISBN (Print)
- 978-1-83558-131-5
- ISBN (Online)
- 978-1-83558-132-2
- Published Date
- 17 November 2023
- Series
- Theoretical and Natural Science
- ISSN (Print)
- 2753-8818
- ISSN (Online)
- 2753-8826
- DOI
- 10.54254/2753-8818/10/20230325
- Copyright
- 17 November 2023
- Open Access
- This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited