Geodesic
Symmetries in quaternionic analysis
Matematičeskie zametki SVFU, Tome 29 (2022) no. 1, pp. 88-102 Cet article a éte moissonné depuis la source Math-Net.Ru

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This survey-type paper deals with the symmetries related to quaternionic analysis. The main goal is to formulate an $SU$ (2) invariant version of the theory. First, we consider the classical Lie groups related to the algebra of quaternions. After that, we recall the classical Spin(4) invariant case, that is Cauchy-Riemann operators, and recall their basic properties. We define the $SU$ (2) invariant operators called the Coifman-Weiss operators. Then we study their relations with the classical Cauchy-Riemann operators and consider the factorization of the Laplace operator. Using $SU$ (2) invariant harmonic polynomials, we obtain the Fourier series representations for quaternionic valued functions studying in detail the matrix coefficients.
Keywords: quaternionic analysis, Cauchy–Riemann operator, Coif-man–Weiss operator, Fourier series
Mots-clés : Lie group SU (2), matrix element. 
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     author = {H. Orelma},
     title = {Symmetries in quaternionic analysis},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {88--102},
     year = {2022},
     volume = {29},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2022_29_1_a6/}
}
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H. Orelma. Symmetries in quaternionic analysis. Matematičeskie zametki SVFU, Tome 29 (2022) no. 1, pp. 88-102. http://geodesic.mathdoc.fr/item/SVFU_2022_29_1_a6/