| Clifford algebra approach to pointwise convergence of Fourier series on spheres Dedicated to Professor Sheng GONG on the occasion of his 75th birthday |
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| 作者姓名： | FEI Minggang & QIAN Tao Faculty of Science and Technology University of Macau P.O. Box Macao China |
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| 作者单位： | FEI Minggang & QIAN Tao Faculty of Science and Technology，University of Macau，P.O. Box 3001，Macao，China |
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| 摘 要： | We offer an approach by means of Clifford algebra to convergence of Fourier series on unit spheres of even-dimensional Euclidean spaces. It is based on generalizations of Fueter's Theorem inducing quaternionic regular functions from holomorphic functions in the complex plane. We, especially, do not rely on the heavy use of special functions. Analogous Riemann-Lebesgue theorem, localization principle and a Dini's type pointwise convergence theorem are proved.
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Clifford algebra approach to pointwise convergence of Fourier series on spheres Dedicated to Professor Sheng GONG on the occasion of his 75th birthday |
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| FEI Minggang & QIAN Tao Faculty of Science and Technology,University of Macau,P.O. Box ,Macao,China.Clifford algebra approach to pointwise convergence of Fourier series on spheres Dedicated to Professor Sheng GONG on the occasion of his 75th birthday[J].Science in China(Mathematics),2006(11). |
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| Authors: | FEI Minggang & QIAN Tao Faculty of Science and Technology University of Macau PO Box Macao China |
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| Institution: | FEI Minggang & QIAN Tao Faculty of Science and Technology,University of Macau,P.O. Box 3001,Macao,China |
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| Abstract: | We offer an approach by means of Clifford algebra to convergence of Fourier series on unit spheres of even-dimensional Euclidean spaces. It is based on generalizations of Fueter's Theorem inducing quaternionic regular functions from holomorphic functions in the complex plane. We, especially, do not rely on the heavy use of special functions. Analogous Riemann-Lebesgue theorem, localization principle and a Dini's type pointwise convergence theorem are proved. |
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| Keywords: | Clifford algebra pointwise convergence of Fouirer series unit sphere Fueter's Theorem |
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