Abstract
We offer a new approach to convergence of Fourier series on the unit sphere of the four-dimensional Euclidean space. The approach is via the quaternionic analysis setting with a crucial application of Fueter’s theorem. Analogs to the Riemann-Lebesgue theorem, localization principle and a Dini’s type pointwise convergence theorem are proved.
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Liu, S., Qian, T. (2004). Pointwise Convergence of Fourier Series on the Unit Sphere of R4 with the Quaternionic Setting. In: Qian, T., Hempfling, T., McIntosh, A., Sommen, F. (eds) Advances in Analysis and Geometry. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7838-8_7
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DOI: https://doi.org/10.1007/978-3-0348-7838-8_7
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9589-7
Online ISBN: 978-3-0348-7838-8
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