Pointwise convergence for expansions in spherical monogenics
Fei M.1; Qian T.2
Source PublicationActa Mathematica Scientia

We offer a new approach to deal with the pointwise convergence of Fourier-Laplace series on the unit sphere of even-dimensional Euclidean spaces. By using spherical monogenics defined through the generalized Cauchy-Riemann operator, we obtain the spherical monogenic expansions of square integrable functions on the unit sphere. Based on the generalization of Fueter's theorem inducing monogenic functions from holomorphic functions in the complex plane and the classical Carleson's theorem, a pointwise convergence theorem on the new expansion is proved. The result is a generalization of Carleson's theorem to the higher dimensional Euclidean spaces. The approach is simpler than those by using special functions, which may have the advantage to induce the singular integral approach for pointwise convergence problems on the spheres. 

Keyword30g35 42b05 Generalization Of Fueter's Theorem Generalized Cauchy-riemann Operator Pointwise Convergence Of Fourier-laplace Series Spherical Monogenics Unit Sphere
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Indexed BySCIE
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000270313100012
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Affiliation1.University of Electronic Science and Technology of China
2.Universidade de Macau
Recommended Citation
GB/T 7714
Fei M.,Qian T.. Pointwise convergence for expansions in spherical monogenics[J]. Acta Mathematica Scientia,2009,29(5):1241-1250.
APA Fei M.,&Qian T..(2009).Pointwise convergence for expansions in spherical monogenics.Acta Mathematica Scientia,29(5),1241-1250.
MLA Fei M.,et al."Pointwise convergence for expansions in spherical monogenics".Acta Mathematica Scientia 29.5(2009):1241-1250.
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